Midterm exercise

Question 1

Mart's Boutique has sales of $820,000 and costs of $540,000. Interest expense is $36,000 and depreciation is $59,000. The tax rate is 35 percent. What is the net income?
A. $99,600
B. $120,250
C. $158,600
D. $105,000
E. $179,250

Answer 1

Sales                  $820,000
Costs                    540,000
Depreciation          59,000
----
EBIT                    $221,000
Interest                   36,000
----
EBT                      $185,000
Tax                           64,750
----
Net income          $120,250

Question 2

Your firm has total sales of $22,980, costs of $14,715, and depreciation of $6,045. The tax rate is 34 percent. There are no interest expenses or other income. What is the "operating cash flow"?
A. $7,510.20
B. $1,465.20
C. $8,340.00
D. $9,019.80
E. $2,410.80

Answer 2

Sales              $22,980
Costs                14,715
Depreciation    6,045
----
EBIT                   2,220
Tax                        754.8
----
Net income        1,465.2
(chú ý đề hỏi OCF, not NI)
OCF = EBIT + Depr. - Tax = 2,220+6,045-754.=7,510.2

Question 3

Wybro’s Markets has sales of $684,000, costs of $437,000, interest paid of $13,800, total assets of $712,000, and depreciation of $109,400. The tax rate is 35 percent and the equity multiplier is 1.6. What is the return on equity?

a. 13.92%
b. 15.48%
c. 7.06%
d. 11.30%
e. 18.08%

Answer 3

Sales             684,000
Costs             437,000
Depreciation 109,400
---
EBIT                137,600             
Interest             13,800
---
EBT                  123,800
Tax                     43,330
--- 
Net income        80,470

Equity multiplier = TA/TE
<=> 1.6 = 712,000 (de cho)/TE
=> TE = 445,000

ROE = NI / TE
=80,470 (inc st)/445,000=18.08%

Question 4

Puffy's Pastries generates five cents of net income for every $1 in equity. Thus, Puffy's has \_\_\_\_\_\_\_ of 5 percent.
A. an EV multiple
B. a return on assets
C. a profit margin
D. a price-earnings ratio
E. a return on equity

Answer 4

5 cents -> $0.05

ROE = NI/TE = 0.05/1 = 5%

Question 5

Uptowne Restaurant has sales of $418,000, total equity of $224,400, a tax rate of 34 percent, a debt-equity ratio of .37, and a profit margin of 5.1 percent. What is the return on assets?
A. 6.93%
B. 9.50%
C. 11.08%
D. 7.13%
E. 13.13%

Answer 5

*ROA = NI/TA = 21,318/307,428 = 6.93%

Profit margin = NI/sales
<=> 5.1% = NI/418,000
=> NI = 21,318

(Equity multiplier =) TA/TE = 1 + D/E
<=> TA/224,400 = 1 + .37
=> TA = 307,428

Question 6

Sun Shade's has sales of $363,000, total assets of $323,500, and a profit margin of 14.6 percent. The firm has a total debt ratio of 54 percent. What is the return on equity?
A. 28.45%
B. 35.61%
C. 23.29%
D. 31.74%
E. 7.88%

Answer 6

*ROE = NI/TE = 52,998/148,810 = 35.61%

Profit margin = NI/sales
<=> 14.6% = NI/363,00
=> NI = 52,998

Total debt ratio = (TA-TE)/TA
<=> 54% = (323,500-TE)/323,500
=> TE = 148,810

Question 7

Frederico's has a net income of $29,600, a total asset turnover of 1.4, total assets of $318,600, and a debt-equity ratio of .35. What is the return on equity?
A. 16.72%
B. 8.40%
C. 12.54%
D. 14.67%
E. 17.56%

Answer 7

*ROE = NI/TE = 29,600/236,000 = 12.54%

total asset turnover = sales/TA
<=> 1.4 = sales/318,600
=> sales = 446,040

(Equity multiplier =) TA/TE = 1 + D/E
<=> 318,600/TE = 1 + .35
=> TE = 236,000

Question 8

Samuelson's has sales of $317,000, a profit margin of 8.6 percent, an equity multiplier of 1.8, and total debt of $144,400. What is the return on equity?
A. 15.48%
B. 14.46%
C. 7.05%
D. 15.10%
E. 11.25%

Answer 8

*ROE = NI/TE = 27,262/180,500 = 15.10 %

Profit margin = NI/sales
<=> 8.6% = NI/317,000
=> NI = 27,262

Equity multiplier = 1 + D/E
<=> 1.8 = 1 + D/E
=> D/E = .8

D/E=TD/TE
<=> .8=144,400/TE
=> TE=180,500

Question 9

The net present value of a project is equal to the

Answer 9

present value of the future cash flows minus the initial cost

Question 10

(?) You are comparing two investment options, each of which will provide $15,000 of total income. Option A pays five annual payments starting with $5,000 the first year followed by four annual payments of $2,500 each. Option B pays five annual payments of $3,000 each. Which one of the following statements is correct given these two investment options?

Answer 10

C. Given a positive rate of return, Option A is worth more today than Option B

PV=15,000

A:
C=5,000
T=4
-> r=0.416

B:
C=3,000
T=5
-> r=0.262

Question 11

Olivia is willing to pay $185 a month for four years for a car payment. If the interest rate is 4.9 percent, compounded monthly, and she has a cash down payment of $2,500, what price car can she
afford to purchase?

Cash down: tiền trả ngay

Answer 11

(compounded monthly) annuity, C=185, r = 4.9%/12, T=4x12
PV=C/r x [1-1/(1+r)^T] = 185/(4.9%/12) x [1-1/(1+4.9%/12)^4x12] = 8,049.07

Total price of the car can afford: $8049.07 + $2,500 (down payment) = $10,549.07

Question 12

Theo is depositing $1,300 today in an account with an expected rate of return of 8.1 percent.

If he deposits (gửi tiền vào ngân hàng) an additional $3,200 “two years from today”,

and $4,000 “three years from today”, what will
his account balance be ten years from today?

Answer 12

FV = 1,300(1+0.081)^10
+ 3,200(1+0.081)^8
+ 4,000*(1+0.081)^7 = $15,699.54

Question 13

The government imposed a fine on the Not-So-Legal Company.

The fine calls for a payment of $100,000 today, $150,000 “one year from today”, and $200,000 “two years from today”.

(The government will hold the funds until the final payment is collected and then donate the entire amount to charity. )

The government has agreed to pay annual interest of 3 percent on the held funds. How much will be donated to charity in “two years”?

Answer 13

FV = 100,000(1+0.03)^2
+ 150,000(1+0.03)^1
+ 200,000 = $460,590

Question 14

A firm has $820 in inventory, $3,200 in fixed assets, $1,210 in accounts receivable, $890 in accounts payable, and $360 in cash. What is the amount of the net working capital?
A) $4,700
B) $1,500
C) $3,600
D) $2,390
E) $5,590
B) $1,500

Answer 14

NWC = CA - CL=2,390-890=1,500

CA= Inventory + AR + Cash = 820 + 1,210 + 360=2,390

CL = AP = 890

Question 15

Oscar’s Dog Treats had a cash flow to creditors of $2,840, a cash flow to stockholders of $1,630 last year. The firm spent a net of $1,420 on fixed assets and reduced net working capital by $330. What was the operating cash flow?

Answer 15

OCF = 2,840+1,630+1,420-330 = 5,560

Question 16

Woodlands Inc.
2015 Income Statement
($ in millions)
Total operating revenues $3,806
Cost of goods sold 2,315
Selling, general, and administrative expenses 546
Depreciation 311
________________________________________
Earnings before interest and taxes (EBIT) $634
Interest expense 170
________________________________________
Pretax income $464
Taxes 162
________________________________________
Net income $302

Answer 16

OCF = EBIT + Depreciation - Tax = 634+311-162 = 783

Question 17

Your firm has total sales of $22,980, costs of $14,715, and depreciation of $6,045. The tax rate is 34 percent. There are no interest expenses or other income. What is the operating cash flow?

Answer 17

EBIT=sales-costs-depreciation= -> store A
Tax= A x tax rate = -> store B

OCF = A + Depreciation - B = $7,510.20

Question 18

Mart’s Boutique has sales of $820,000 and costs of $540,000. Interest expense is $36,000 and depreciation is $59,000. The tax rate is 35 percent. What is the net income?

Answer 18

EBIT=sales-costs-depreciation=221,000
EBT=EBIT-Interest=185,000
Tax=EBTx35%=64,750
NI=EBT-Tax=$120,250

Question 19

At the beginning of the year, a firm has current assets of $16,200 and current liabilities of $13,280.

At the end of the year, the current assets are $14,800 and the current liabilities are $14,210. What is the change in net working capital?

Answer 19

change in net working capital= NWC (end) - NWC (beg) = −$2,330

Question 20

(??) Last year, Webster Farms had annual revenue of $87,200, depreciation of $11,600, cost of goods sold of $54,700, and administrative expenses of $8,300. The firm paid $3,200 in dividends and paid taxes of $4,300. What was the operating cash flow?

A) $8,300
B) $23,100
C) $16,700
D) $19,900
E) $11,500

Answer 20

EBIT=revenue-COGS-depreciation-administrative expenses=12,600

D) $19,900

Question 21

Uptowne Restaurant has sales of $418,000, total equity of $224,400, a tax rate of 34 percent, a debt-equity ratio of .37, and a profit margin of 5.1 percent. What is the return on assets?

Answer 21

ROA = Net income/TA = 6.93%

Profit margin = NI/sales
<=> 5.1% = NI/418,000
=> NI = 21,318

Equity multiplier = TA/TE = 1 + D/E
<=> TA/224,400 = 1 + .37
=> TA = 307,428

Question 22

Frederico’s has a net income of $29,600, a total asset turnover of 1.4, total assets of $318,600, and a debt-equity ratio of .35. What is the return on equity

Answer 22

ROE = NI/TE = 29,600/236,000 = 12.54%

equity multiplier = TA/TE = 1 + D/E
<=> 318,600/TE = 1 + .35
=> TE = 236,000

Question 23

Wybro’s Markets has sales of $684,000, costs of $437,000, interest paid of $13,800, total assets of $712,000, and depreciation of $109,400. The tax rate is 35 percent and the equity multiplier is 1.6. What is the return on equity?

Answer 23

ROE = NI/TE = 80,470/445,000 = 18.08%

EBIT=sales-costs-depreciation=137,600
EBT=EBIT-interest=137,600-13,800=123,800
Tax=EBTx35%=43,330
NI=EBT-Tax=123,800-43,330=80,470

Equity multiplier = TA/TE
<=> 1.6 = 712,000/TE
=> TE = 445,000

Question 24

Samuelson’s has sales of $317,000, a profit margin of 8.6 percent, an equity multiplier of 1.8, and total debt of $144,400. What is the return on equity? -> 15.10%

Answer 24

ROE = NI/TE = 27,262/180,500 = 15.10%

Profit margin = NI/sales
<=> 8.6% = NI/317,000
=> NI = 27,262

**TA-TE=TD -> TA = TD + TE (đưa về unit đã có và đang tìm) = 144,400 + TE
Equity multiplier = TA/TE
EQ = (TD+TE)/TE
1.8 = (144,400+TE)/TE
=> TE = 180,500

Question 25

A firm has a return on equity of 16.2 percent, a debt-equity ratio of 44 percent, a capital intensity ratio of 1.08, a current ratio of 1.25, and current assets of $138,000. What is the profit margin? -> 12.15%

Answer 25

*Profit margin = NI/sales=15,525/127,777.(7)=12.15%

(2)
ROE = NI/TE
<=> 16.2% = NI/95,8333.(3)
=> NI=15,525

(1)
capital intensity ratio = TA/Sales or revenue
<=> 1.08 = 138,000/Sales
=> Sales=127,777.(7)

(1)
TA/TE=1+D/E=1.44
TA/TE=138,000/TE=1.44
=> TE=95,833.(3)

(? CL ko dùng
current ratio = CA/CL
1.25=138,000/CL
=> CL=110,400)

Question 26

Sun Shade’s has sales of $363,000, total assets of $323,500, and a profit margin of 14.6 percent. The firm has a total debt ratio of 54 percent. What is the return on equity? -> 35.61%

Answer 26

ROE = NI/TE = 52,998/148,810 = 35.61%

Profit margin = NI/sales
<=> 14.6% = NI/363,000
=> NI = 52,998

Total debt ratio = (TA-TE)/TA
<=> 54%=(323,500-TE)/323,500
=> TE=148,810

Question 27

Northern Industries has accounts receivable of $42,300, inventory of $61,200, sales of $544,200, and cost of goods sold of $393,500. How many days, on average, does it take the firm to sell its inventory? -> 56.77

Answer 27

Days’ Sales in Inventory = 365/Inventory turnover=365/6.4297=56.77

Inventory turnover=COGS/Inventory=393,500/61,200=6.4297

Question 28

Catherine’s Consulting has net income of $4,400 and total equity of $39,450. The debt-equity ratio is 1 and the plowback ratio is 40 percent. What is the return on assets? -> 5.58%

Answer 28

ROA=Net income/TA = 4,400/78,900=5.58%

Equity multiplier = TA/TE = 1 + D/E
<=> TA/39,450 = 1 + 1
=> TA =78,900

Question 29

You are comparing two investment options, each of which will provide $15,000 of total income. Option A pays five annual payments starting with $5,000 the first year followed by four annual payments of $2,500 each. Option B pays five annual payments of $3,000 each. Which one of the following statements is correct given these two investment options?

Answer 29

Given a positive rate of return, Option A is worth more today than Option B.

annual payment -> annuity

PV=15,000
C(A)=5,000
C(B)=2,500
 -> thế vào CT annuity shift solve ra r(A), r(B)
-> r(A) lớn hơn -> chọn r(A)

Question 30

Assume you graduate with $31,300 in student loans at an interest rate of 5.25 percent, compounded monthly. If you want to have this debt paid in full within three years, how much must you pay each month? -> $941.61

Answer 30

(Compounded monthly) Annuity:
$31,300 = C × [(1 - {1 / [1 + (.0525 / 12)] 3 × 12}) / (.0525 / 12)]; C = $941.61

compounded monthly

• > r=5.25%/12
• > T=3x12=36 months

Question 31

Denise will receive annual payments of $10,000 for the next 25 years. The discount rate is 6.8 percent. What is the difference in the present value of these payments if they are paid at the beginning of each year rather than at the end of each year? -> $8,069

Answer 31

C1:
PV(end) = [$10,000 × ({1 - [1 / (1 + .068) 25]} / .068)]
= $118,665.92

Difference = .068 × $118,665.92 = $8,069.28

C2:
PV(beg) = [$10,000 × ({1 - [1 / (1 + .068) 25]} / .068)]
× (1 + .068)
= $126,735.21

PV(end) = [$10,000 × ({1 - [1 / (1 + .068) 25]} / .068)]
= $118,665.92

Difference = $126,735.21 - 118,665.92 = $8,069.29

Question 32

An annuity costs $70,000 today, pays $3,500 a year, and earns a return of 4.5 percent. What is the length of the annuity time period? -> 52.31 years

Answer 32

thế PV=70,000, C=3,500, r=4.5% vào CT annuity -> T=52.31

Question 33

You just paid $525,000 for a security that will pay you and your heirs $25,000 a year forever. What rate of return will you earn? -> 4.76%

Answer 33

thế PV=525,000, C=25,000 vào (forever) Perpetuity: PV=C/r -> r=4.76%

Question 34

(?) You want to save sufficient funds to generate an annual cash flow of $55,000 a year for 25 years as retirement income. You currently have no retirement savings but plan to save an equal amount each year for the next 38 years until your retirement. How much do you need to save each year if you can earn 7.5 percent on your savings? -> $3,146.32

Answer 34

C=55,000; T=25, r=7.5%
T(save)=38; r=7.5%

PV(annuity) = $55,000 × ({1 - [1 / (1 + .075) 25]} / .075) = $613,082.02

(?) $613,082.02 = C/.75 × [(1 + .075)^38 −1] ;
-> C = $3,146.32

Question 35

You are borrowing $5,200 at 7.8 percent, compounded monthly. The monthly loan payment is $141.88. How many loan payments must you make before the loan is paid in full? -> 42

Answer 35

thế PV=5,200; C=141.88, r=7.8%/12, T=? vào CT annuity -> T(month)=42

Question 36

You are considering two insurance settlement offers. The first offer includes annual payments of $36,000, $42,000, and $50,000 over the next three years, respectively, with the first payment being made one year from today. The other offer is the payment of one lump sum amount today. The relevant discount rate is 7 percent. What is the minimum amount you should accept today if you are to select the lump sum offer? -> $111,144.18

(lump sum: thuế gộp)

Answer 36

PV = $36,000 / 1.07 + $42,000 / 1.07^2 + $50,000 / 1.07^3 = $111,144.18

Question 37

Starting today, Alicia is going to contribute $100 a month to her retirement account. Her employer matches her contribution by 50 percent. If these contributions remain constant, and she earns a monthly rate of .55 percent, how much will her savings be worth 40 years from now? -> $354,087.88

Answer 37

AFV = ($100 + 50)/.0055 ×

[(1 + .0055)^(40 × 12) − 1] × (1 + .0055) = $354,087.88

Question 38

Assume mortgage rates increase to 7.5 percent and you borrow $329,000 for 30 years to purchase a house. What will your loan balance be at the end of the first 15 years of payments?

Answer 38

r=7.5%, PV(30yrs)=329,000, T=30

(CT annuity) 329,000=C/(7.5%/12)x[(1-1/(1+7.5%/12)^30x12)] => C=2,300.4157

(CT annuity) PV(15yrs)=2,300.4157/(7.5%/12)x[(1-1/(1+7.5%/12)^15x12)] = $248,153.73

Question 39

You borrow $199,000 to buy a house. The mortgage rate is 5.5 percent, compounded monthly. The loan period is 30 years, and payments are made monthly. If you pay for the house according to the loan agreement, how much total interest will you pay?

Answer 39

$199,000 = C × [(1 - {1 / [1 + (.055 / 12)] 30 × 12}) / (.055 / 12)]; C = $1,129.90 Total interest = (30 × 12 × $1,129.90) −$199,000 = $207,764

Question 40

Jeanette expects to live 30 years after she retires. At the end of the first year of her retirement, she wants to withdraw $35,000 from her savings. Each year thereafter, she wants to increase her annual withdrawal by 3.5 percent. If she can earn 5.5 percent on her savings, how much does she need to have in retirement savings on the day she retires?

Answer 40

PV = $35,000 ×
(1 -
[(1 + .035) / (1 + .055)]^30) / (.055 - .035)] = $764,458.87

Question 41

Lois is purchasing an annuity that will pay $5,000 annually for 20 years, with the first annuity payment made on the date of purchase. What is the value of the annuity on the purchase date given a discount rate of 7 percent? -> $56,677.98

Answer 41

(CT annuity) PV = [$5,000 × ({1 - [1 / (1 + .07) 20]} / .07)] × (1 + .07) = $56,677.98
“the first annuity payment made on the date of purchase” -> nhân thêm với (1+7%)

Question 42

You expect an investment to return $11,300, $14,600, $21,900, and $38,400 annually over the next four years, respectively. What is this investment worth to you today if you desire a rate of return of 16.5 percent?

Answer 42

PV = $11,300 / 1.165 + $14,600 / 1.165^2 + $21,900 / 1.165^3 + $38,400 / 1.165^4 = $55,153.57

PV=FV(1+r)^t

Question 43

Shawn has $2,500 invested at a guaranteed rate of 4.35 percent, compounded annually. What will his investment be worth after five years? -> 3,093.16

Answer 43

(chỉ nói là invest, ko có a year/month… -> ko phải annuity)
FV=PV(1+r)^t=2,500(1+4.35%)^5=$3,093.16

Question 44

Theo is depositing $1,300 today in an account with an expected rate of return of 8.1 percent. If he deposits an additional $3,200 two years from today, and $4,000 three years from today, what will his account balance be ten years from today?

Answer 44

FV = $1,300 ×1.081^10
+ $3,200 ×1.081^8 (“two years from today” -> 10-2=8)
+ $4,000 ×1.081^7 (“three years from today” -> 10-3=7)
= $15,699.54

Question 45

Suzette is receiving $10,000 today, $15,000 one year from today, and $25,000 four years from today. She will immediately invest these funds for retirement. If she earns 9.6 percent on her investments, how much will she have in savings 30 years from today?

Answer 45

FV = $10,000 × 1.096^30
+ $15,000 × 1.096^29 (“one year from today” -> 30-1=29)
+ $25,000 × 1.096^26 = $641,547.39 (“four years from today” -> 30-4=26)

Question 46

You are considering a project with projected annual cash inflows of $32,200, $41,800, $22,900 for the next three years, respectively. What is the value of the project today at a discount rate of 14 percent?

Answer 46

PV = $32,200 / 1.14 + $41,800 / 1.14^2 + $22,900 / 1.14^3 = $75,866.20

Question 47

Donaldson’s purchased some property for $1.2 million, paid 25 percent down in cash, and financed the balance for 12 years at 7.2 percent, compounded monthly. What is the amount of each monthly mortgage payment?

Answer 47

Amount financed = $1,200,000 ×(1 −.25) = $900,000

$900,000 = C × [(1 - {1 / [1 + (.072 / 12)] 12 × 12}) / (.072 / 12)]; C = $9,351.66

Question 48

You are buying a car for $7,500, paying $900 down in cash, and financing the balance for 24 months at 6.5 percent, compounded monthly. What is the amount of each monthly loan payment?

Answer 48

Amount financed = $7,500 −900 = $6,600

$6,600 = C × [(1 - {1 / [1 + (.065 / 12)] 24}) / (.065 / 12)]; C = $294.01

Question 49

You are comparing two annuities with equal present values. The applicable discount rate is 6.5 percent. One annuity will pay $2,000 annually, starting today, for 20 years. The second annuity will pay annually, starting one year from today, for 20 years. What is the annual payment for the second annuity?

Answer 49

C1:
C = $2,000 (trong de) × 1.065 (trong de) = $2,130

C2:
APV ADue = [$2,000 × ({1 - [1 / (1 + .065) 20]} / .065)] × (1 + .065) = $23,469.42

$23,469.42 = [ C × ({1 - [1 / (1 + .065) 20]} / .065)]; C = $2,130

Question 50

What is the effective annual rate of 13.52 percent compounded continuously? -> 14.48%

Answer 50

EAR = (e^.1352) - 1 = .1448

Question 51

Leo received $7,500 today and will receive another $5,000 two years from today. He will invest these funds when he receives them and expects to earn a rate of return of 11.5 percent. What value does he expect his investments to have five years from today?

Answer 51

FV = $7,500 × 1.115^5 (“today”)
+ $5,000 × 1.115^3 (“two years from today” -> 5-2=3)
= $19,856.13

Question 52

Stu can purchase a one-bedroom house near his college today for $110,000, including the cost of some minor repairs. He expects to be able to resell it in four years for $150,000 if he just puts a little effort into cleaning up the property. At a discount rate of 6.5 percent, what is the expected net present value of this purchase opportunity?

Answer 52

NPV = −$110,000 + $150,000 / (1 + .065)^4 = $6,598.46

Question 53

Thirty-five years ago, your father invested $2,000. Today that investment is worth $98,407. What rate of return has your father earned on his investment? -> 11.77%

Answer 53

$98,407 = $2,000 ×(1 + r) ^35; r = .1177, or 11.77% (thế đáp án)

Question 54

Consider a bond with a coupon rate of 8 percent that pays semiannual interest and matures in eight years. The market rate of return on bonds of this risk is currently 11 percent. What is the current value of a $1,000 face value bond? -> $843.07

Answer 54

“market rate of return on bonds of this risk” -> YTM
“semiannually” -> r=8%/2, YTM=11%/2, N=8x2
C or PMT = FV x Coupon rate = 1,000 x 8%/2

Bond value = [(.08 × $1,000) / 2] × [(1 - {1 / [1 + (.11 / 2)] 8 ×2}) / (.11 / 2)] + $1,000 / [1 + (.11 / 2)] 8 × 2 = $843.07

Question 55

A corporate bond with a face value of $1,000 matures in 4 years and has a coupon rate of 6.25 percent. The current price of the bond is $932 and interest is paid semiannually. What is the yield to maturity? -> 8.28%

Answer 55

“semiannually” -> YTM/2, r/2, Nx2
C or PMT=FV x coupon rate
$932 = [(.0625 × $1,000) / 2] × [(1 - {1 / [1 + (YTM / 2)] 4 × 2}) / (YTM / 2)] + $1,000 / [1 + (YTM / 2)] 4 × 2; YTM = 8.28%

Question 56

The Lo Sun Corporation offers a bond with a current market price of $1,029.75, a coupon rate of 8 percent, and a yield to maturity of 7.52 percent. The face value is $1,000. Interest is paid semiannually. How many years is it until this bond matures? -> 8.5 years

Answer 56

“semiannually” -> YTM/2, r/2, tx2

$1,029.75 = [(.08 / 2) × $1,000] × [(1 - {1 / [1 + (.0752 / 2)] t × 2}) / (.0752 / 2)] + $1,000 / [1 + (.0752 / 2)] t × 2;
t=8.5 years

Question 57

Westover’s has an outstanding bond with a coupon rate of 5.5 percent that matures in 12 years. The bond pays interest semiannually. What is the market price of a $1,000 face value bond if the yield to maturity is 7.13 percent? -> $870.01

Answer 57

“semiannually” -> YTM/2, r/2, Nx2

Bond price = [(.055 / 2) × $1,000] × [(1 - {1 / [1 + (.0713 / 2)] ^(12 × 2)}) / (.0713 / 2)] + $1,000 / [1 + (.0713 / 2)] ^(12 × 2) = $870.01

Question 58

Otto Enterprises has a 15-year bond issue outstanding with a coupon of 8 percent. The bond is currently priced at $923.60 and has a par value of $1,000. Interest is paid semiannually. What is the yield to maturity?

Answer 58

“semiannually” -> YTM/2, r/2, Nx2

Response Feedback: $923.60 = [(.08 / 2) × $1,000] × [(1 - {1 / [1 + (YTM / 2)] ^(15 × 2)}) / (YTM / 2)] + $1,000 / [1 + (YTM / 2)] ^(15 × 2); YTM = 8.93%

Question 59

A $1,000 par value bond carries a coupon rate of 6.5 percent and has a yield to maturity of 7.29 percent. The inflation rate is 3.13 percent. What is the bond’s real rate of return?

Answer 59

*YTM=nominal=7.29%
(1+nominal) = (1+real) (1+inflation)
(1+7.29%)=(1+x)(1+3.13%) -> r=4.03%

Question 60

TJ’s offers a $1,000 face value, zero coupon bond with a yield to maturity of 11.3 percent, given annual compounding. The bond matures in 16 years. What is the current price?

Answer 60

zero coupon bond -> PV=F/(1+r)^t

Price = $1,000 / (1 + .113) ^16 = $180.33

Question 61

MJ Enterprises stock traditionally provides an average rate of return of 11.6 percent. The firm’s next annual dividend is projected at $2.40 with future increases of 3 percent per year. What price should you pay for this stock is you are satisfied with the firm’s average rate of return? -> $27.91

Answer 61

“future increases” -> constant growth
“next annual dividend” -> Div1
P0 = $2.40 / (.116 - .03) = $27.91

Question 62

Last year, Logistics paid an annual dividend of $2.20 and announced that all future dividends would be $2.25 a share indefinitely. What is your required rate of return if you are willing to pay $15.25 a share for this stock? -> 14.75%

Answer 62

“willing to pay” -> P0=$15.25
“future dividends” -> Div=$2.25

zero growth: P0=Div/R
R = Div/P0 = $2.25 / $15.25 = .1475

Question 63

(?) City Movers announced that its next annual dividend will be $.40 a share. The following dividends will be $.60, and $.75 a share annually for the following two years, respectively. After that, dividends are projected to increase by 3.5 percent per year. How much is one share of this stock worth at a rate of return of 12 percent?

Answer 63

Div1=$.40, Div2=$.60, Div3=$.75
g=3.5 %
R=12%

P 0 = 
$.40 / 1.12
\+ $.60 / 1.12 ^(2)
\+ $.75 / 1.12 ^(3) 
\+ {[$.75 × (1 + .035)] / (.12 - .035)} / 1.12 ^(3)
P 0 = $7.87

Question 64

Engine Builders stock sells for $24.20 a share. The firm just paid an annual dividend of $2 per share and has a long-established record of increasing its dividend by a constant 2.5 percent annually. What is the market rate of return on this stock?

Answer 64

“just paid” -> Div0=$2
“stock sells” -> P0=$24.20
“increasing its dividend by a constant 2.5 percent” -> g

constant growth CT
P0 = Div1/(R-g) = Div0(1+g)/(R-g) -> R = 10.97 %

Question 65

BC ‘n D just paid its annual dividend of $.60 a share. The projected dividends for the next five years are $.30, $.50, $.75, $1.00, and $1.20, respectively. After that time, the dividends will be held constant at $1.40. What is this stock worth today at a discount rate of 14 percent?

Answer 65

P 0 = $.30 / 1.14 
\+ $.50 / 1.14 ^2 
\+ $.75 / 1.14 ^3 
\+ $1.00 / 1.14 ^4 
\+ $1.20 / 1.14 ^5 
\+ ($1.40 / .14) / 1.14 ^5 = $7.56

Question 66

How much are you willing to pay for one share of stock if the company just paid an annual dividend of $1.03, the dividends increase by 3 percent annually, and you require a rate of return of 15 percent?

Answer 66

Div0=$1.03
g=3 percent
R=15 percent

Constant growth
P 0 = ($1.03 x (1+.03)) / (.15 - .03) = $8.84

Question 67

The Bell Weather Co. is a new firm in a rapidly growing industry. The company is planning on increasing its annual dividend by 20 percent next year and then decreasing the growth rate to a constant 5 percent per year. The company just paid its annual dividend in the amount of $1 per share. What is the current value of a share if the required rate of return is 14 percent?

Answer 67

g1=20 percent (next yr)
g=5 percent
Div0=$1
R=14 percent

P 0
= [$1 × (1 + .20)] / 1.14
+ {[($ × (1 + .20) × (1 + .05)] / (.14 - .05)} / 1.14 = $13.33

Question 68

You have decided to purchase shares of GHC but need an expected 12 percent rate of return to compensate for the perceived risk of such ownership. What is the maximum price you should pay per share if the company pays a constant $2.70 annual dividend

Answer 68

R=12 percent
Div=$2.70

“pays a constant” -> zero growth
P0 = $2.70 / .12 = $22.50

Question 69

The common stock of Fine China sells for $38.42 a share. The stock is expected to pay an annual dividend of $1.80 next year and increase that amount by 4 percent annually thereafter. What is the market rate of return on this stock?

Answer 69

P0=$38.42
“expected” -> Div1=$1.80
g=4 percent

constant growth:
P0=Div1/(R-g)
-> R = $1.80 / $38.42 + .04 = .0869, or 8.69%

Question 70

T&P common stock sells for $23.43 a share at a market rate of return of 11.65 percent. The company just paid its annual dividend of $1.20. What is the dividend growth rate?

Answer 70

“stock sells” -> P0=$23.43
R=11.65 percent
“just paid” -> Div0=$1.20

constant growth:
P0 = Div1/(R-g) = (Div0(1+g))/(R-g)
P0 = $23.43 = $1.20 × (1 + g) / (.1165 - g); g = .0621, or 6.21%

Question 71

Merriweather’s has a policy of increasing its annual dividend by 1.75 percent each year. How much will one share be worth five years from now if the required rate of return is 15 percent and the next dividend will be $3.40?

Answer 71

g=1.75 percent
T=5
R=15 percent
“next dividend” -> Div1=$3.40

Constant growth:
P5 = Div6/(R-g) = (Div0(1+g)^6)/(R-g) = (Div1(1+g)^5)/(R-g)
P5 = [$3.40 × (1 + .0175) ^5] / (.15 - .0175) = $27.99

Question 72

Uptown Clothing just paid $1.50 as its annual dividend and increases its dividend by 2.5 percent each year. What will Uptown’s stock price be in ten years at a discount rate of 12.25 percent?

Answer 72

“just paid” -> Div0=$1.50
g=2.5 percent
R=12.25%

constant growth:
P10 = Div11/(R-g) = (Div0(1+g)^11)/(R-g)
P10 = [$1.50 × (1 + .025) ^11] / (.1225 - .025) = $20.19

Question 73

Last week, Railway Tours paid its annual dividend of $1.20 per share. The company has been reducing the dividends by 10 percent each year. What is the value of this stock at a discount rate of 13 percent?

Answer 73

“paid” -> Div0=$1.20
“reducing the dividends” -> g= - 10 percent
R=13 percent

Constant growth:
P0 = (Div0(1+g))/(R-g)
P0 = {$1.20 ×[1 + (-.10)]} / [.13 - (-.10)] = $4.70

Question 74

Lory Company had net earnings of $127,000 this past year of which $46,200 was paid out in dividends. The company’s equity was $1,587,500. Lory has 200,000 shares outstanding with a current market price of $11.63 per share. Both the number of shares and the dividend payout ratio are constant. What is the required rate of return if the growth rate is 5.6 percent?

Answer 74

“current market price” -> P0=$11.63
g=5.6 percent
R = (Div/P0) + g
= (((Div paid/shares outstanding)x(1+g))/Market price) + g

R = [($46,200 / 200,000) × (1.056)] / $11.63) + .056 = .0770, or 7.70%

Question 75

The dividend yield on Alpha’s common stock is 5.2 percent. The company just paid a $2.10 dividend. The rumor is that the dividend will be $2.30 next year. The dividend growth rate is expected to remain constant at the current level. What is the required rate of return on Alpha’s stock?

Answer 75

Dividend yield = Div1/P0 = .052
g = (div next yr - div just paid)/div just paid

Constant growth:
R = Div1/P0 + g
R = .052 + ($2.30 - 2.10) / $2.10 = .1472, or 14.72%

Question 76

Wilbert’s Clothing Stores just paid a $1.20 annual dividend and increases its dividend by 2.5 percent annually. You would like to purchase 100 shares of stock in this firm but realize that you will not have the funds to do so for another three years. If you desire a 10 percent rate of return, how much should you expect to pay for 100 shares when you can afford to buy this stock? Ignore trading costs.

Answer 76

“just paid” -> Div0=$1.20
g=2.5 percent
R=10 percent

constant growth:
P3 = Div4/(R-g) = (Div0(1+g)^4)/(R-g)
P3 = [$1.20 × (1 + .025) ^4] / (.10 - .025) = $17.66

Purchase cost = 100 ×$17.66 = $1,766

Question 77

(?) Dexter’s has a fixed dividend payout ratio of 40 percent, current net income of $5,200, total assets of $56,400, and total equity of $21,600. Given this information, what estimate would you use as the dividend growth rate if the last dividend paid was $.464 per share?

Answer 77

g = (1 - payout ratio) x (NI/TE)

g = (1 - .40) × ($5,200 / $21,600) = .1444, or 14.44%

Question 78

A stock pays a constant annual dividend and sells for $31.11 a share. If the dividend yield of this stock is 9 percent, what is the dividend amount?

Answer 78

“sells for” -> P0 = $31.11

Dividend yield = .09 = Div/P0 = Div/$31.11 -> Div = $2.80

Question 79

The Merriweather Co. just announced that it will pay a dividend next year of $1.60. The company will then increase its dividend by 10 percent per year for two years after which it will maintain a constant 2 percent dividend growth rate. What is one share worth today at a required rate of return of 14 percent?

Answer 79

P 0 
= $1.60 / 1.14 
\+ [$1.60 × (1 + .10)] / 1.14 ^2 
\+ [$1.60 × (1 + .10) ^2] / 1.14 ^3 
\+ {[$1.60 × (1 + .10) ^2 × (1 + .02)] / (.14 - .02)} / 1.14 ^3 = $15.17

Question 80

A stock pays a constant annual dividend and sells for $31.11 a share. If the dividend yield of this stock is 9 percent, what is the dividend amount?

Answer 80

“sells for” -> P0 = $31.11

Dividend yield = .09 = Div/P0 = Div/$31.11 -> Div = $2.80

Question 81

The Merriweather Co. just announced that it will pay a dividend next year of $1.60. The company will then increase its dividend by 10 percent per year for two years after which it will maintain a constant 2 percent dividend growth rate. What is one share worth today at a required rate of return of 14 percent?

Answer 81

“will pay” -> Div1=$1.60
Differential growth:
P 0
= $1.60 / 1.14
(yr2) + [$1.60 × (1 + .10)] / 1.14 ^2
(yr3) + [$1.60 × (1 + .10) ^2] / 1.14 ^3
(yr4) + {[$1.60 × (1 + .10) ^2 × (1 + .02)] / (.14 - .02)} / 1.14 ^3 = $15.17

Question 82

Martin’s Yachts is expected to pay annual dividends of $1.40, $1.75, and $2.00 a share over the next three years, respectively. After that, the dividend is expected to remain constant. What is the current value per share at a discount rate of 14 percent?

Answer 82

P 0 = $1.40 / 1.14 + $1.75 / 1.14 ^2

+ [$2.00 + ($2.00 / .14)] / 1.14 ^3 = $13.57

Question 83

Nu-Tech is expecting a period of intense growth and has decided to reduce its annual dividend by 10 percent a year for the next two years. After that, it will maintain a constant dividend of $.70 a share. Last year, the company paid $1.80 per share. What is the value of this stock if the required rate of return is 13 percent?

Answer 83

"reduce its annual dividend" -> g = - 10%, T=2
Div=$.70 
Div0=$1.80
R=13 percent
P0=?

P 0 = {$1.80 × [1 + (-.10)]} / 1.13
+ {$1.80 ×[1 + (-.10)] ^2} / 1.13 ^2
+ ($.70 / .13) / 1.13 ^2 = $6.79

Question 84

S&P Enterprises will pay an annual dividend of $2.08 a share on its common stock next year. Last week, the company paid a dividend of $2.00 a share. The company adheres to a constant rate of growth dividend policy. What will one share of S&P common stock be worth ten years from now if the applicable discount rate is 8 percent?

Answer 84

“will pay” -> Div1 = $2.08

g = (div next yr - div paid)/div paid = ($2.08 - 2.00) / $2.00 = .04

P10 = [$2.08 ×(1 + .04) ^10] / (.08 - .04) = $76.97

Question 85

The Felix Corp. will pay an annual dividend of $1.00 next year. The dividend will increase by 12 percent a year for the following two years before growing at 4 percent indefinitely thereafter. If the required rate of return is 10 percent, what is the stock’s current value?

Answer 85

Div 1 = $1.00
Div 1 = $1.00 × 1.12 ^1 = $1.12
Div 1 = $1.00 × 1.12 ^2 = $1.2544

P 0 = $1.00 / 1.10 + $1.12 / 1.10 ^2 + $1.2544 / 1.10 ^3 + [($1.2544 × 1.04) / (.10 - .04)] / 1.10 ^3 = $19.11

Question 86

The common stock of Energy Saver pays an annual dividend that is expected to increase by 4 percent annually. The stock commands a market rate of return of 12 percent and sells for $58.25 a share. What is the expected amount of the next dividend to be paid?

Answer 86

P 0 = $58.25 = Div 1 / (.12 - .04); Div 1 = $4.66

Question 87

The Reading Co. has adopted a policy of increasing the annual dividend on its common stock at a constant rate of 3 percent annually. The last dividend it paid (T = 0) was $.90 a share. What will the company’s dividend be six years from now?

Answer 87

Div 6 = $.90 ×1.03^6 = $1.07

Question 88

Upland Motors recently paid a $1.48 per share annual dividend. Dividends are expected to increase by 2.5 percent annually. What is one share of this stock worth today if the appropriate discount rate is 14 percent?

Answer 88

constant growth:

P 0 = ($1.48 × 1.025) / (.14 - .025) = $13.19

Question 89

A company plans to pay an annual dividend of $.30 a share for two years commencing two years from today. After that time, a constant $1 a share annual dividend is planned indefinitely. Given a required return of 14 percent, what is the current value of this stock?

Answer 89

P 0 = $.30 / 1.14 ^2 + $.30 / 1.14 ^3 + ($1 / .14) / 1.14 ^3 = $5.25

Question 90

Unique Stores common stock pays a constant annual dividend of $1.75 a share. What is the value of this stock at a discount rate of 13.25 percent?

Answer 90

P 0 = $1.75 / .1325 = $13.21

Question 91

New Corp. last paid a $1.50 per share annual dividend. The company is planning on paying $1.62, $1.68, $1.75, and $1.80 a share over the next four years, respectively. After that the dividend will be a constant $2.00 per share per year. What is the market price of this stock if the market rate of return is 15 percent?

Answer 91

P0 = $1.62 / 1.15 + $1.68 / 1.15 ^2 + $1.75 / 1.15 ^3 + $1.80 / 1.15 ^4 + ($2.00 / .15) / 1.15 ^4 = $12.48

Question 92

M&D Enterprises paid its first annual dividend yesterday in the amount of $.28 a share. The company plans to double each annual dividend payment for the next three years. After that time, it plans to pay a constant $2.25 per share indefinitely. What is one share of this stock worth today if the market rate of return on similar securities is 11.5 percent?

Answer 92

Dividends for the next three years are $.56, $1.12, and $2.24.
P0 = $.56 / 1.115 + $1.12 / 1.115 ^2 + $2.24 / 1.115 ^3 + ($2.25 / .115) / 1.115 ^3 = $17.13

Question 93

Martha’s recently paid an annual dividend of $3.60 on its common stock. This dividend increases by 2.5 percent per year. What is the market rate of return if the stock is selling for $32.65 a share?

Answer 93

R = D1/P0 + g = (Div0(1+g))/P0 + g
R = ($3.60 × 1.025) / $32.65 + .025 = .1380, or 13.80%

Question 94

The Elder Co. is in downsizing mode. The company paid a $2.50 annual dividend last year. The company has announced plans to lower the dividend by $.50 a year. Once the dividend amount becomes zero, the company will cease all dividends permanently. The required rate of return is 14.5 percent. What is one share of this stock worth?

Answer 94

Div yr1 = $2.50 - $.50 = $2.00
Div yr2 = $2.00 - $.50 = $1.50
…

P 0 = $2.00 / 1.145 + $1.50 / 1.145 ^2 + $1.00 / 1.145 ^3 + $.50 / 1.145 ^4 = $3.85

Question 95

Rosita’s announced that its next annual dividend will be $1.65 a share and all future dividends will increase by 2.5 percent annually. What is the maximum amount you should pay to purchase a share of this stock if you require a 12 percent rate of return?

Answer 95

P 0 = $1.65 / (.12 - .025) = $17.37

Question 96

Alpha Industries is going to pay $.35, $.50, and $.80 a share over the next three years, respectively. After that, the company has stated that the annual dividend will be $1.25 per share indefinitely. What is this stock worth today at a discount rate of 13.45 percent?

Answer 96

P0 = $.35 / 1.1345 + $.50 / 1.1345 ^2 + $.80 / 1.1345 ^3 + ($1.25 / .1345) / 1.1345 ^3 = $7.61

Question 97

Weisbro and Sons common stock sells for $21 a share and pays an annual dividend that increases by 5 percent annually. The rate of return on this stock is 9 percent. What is the amount of the last dividend paid?

Answer 97

P 0 = $21 = (Div 0 × 1.05) / (.09 - .05); Div 0 = $.80

Question 98

Ancient Industries just paid a dividend of $1.03 a share. The company announced today that it expects to pay $.90 a share next year and a final liquidating dividend of $18.44 in two years. What is one share of this stock worth today if the required rate of return is 16 percent?

Answer 98

P 0 = $.90 / 1.16 + $18.44 / 1.16 ^2 = $14.48

Question 99

A company paid an annual dividend of $.40 a share last month and plans to increase the dividend by 7 percent a year for the next 6 years and then increase it by 4 percent annually thereafter. What is the value of this stock at the end of Year 6 if the discount rate is 11 percent?

Answer 99

P6 = [$.40 × (1 + .07) ^6 × (1 + .04)] / (.11 - .04) = $8.92

Question 100

Lester’s has a return on equity of 11.6 percent, a profit margin of 6.2 percent, and a payout ratio of 35 percent. What is the firm’s growth rate?

Answer 100

g = .116 ×(1 - .35) = .0754, or 7.54%

Question 101

Shares of the Samson Co. offer an expected total return of 12 percent. The dividend is increasing at a constant 3.25 percent per year. What is the value of the next dividend if the stock is selling at $28 a share?

Answer 101

R = .12 = Div1/P0 + g = Div 1 / $28 + .0325 => Div 1 = $2.45

Question 102

Bikes and More just announced its next annual dividend will be $2.42 a share and all future dividends will increase by 2.5 percent annually. What is the market rate of return if this stock is currently selling for $22 a share?

Answer 102

R = Div1/P0 + g = $2.42 / $22 + .025 = .1350, or 13.50%

Question 103

DC Motors recently paid $1.10 as its annual dividend. Future dividends are projected at $1.06 $1.02, and $1.00 over the next three years, respectively. After that, the dividend is expected to decrease by 2 percent annually. What is one share of this stock worth at a rate of return of 17 percent?

Answer 103

g = - .02
R = .17

P 0 = $1.06 / 1.17 + $1.02 / 1.17 ^2 + $1.00 / 1.17 ^3
+ {[$1.00 × (1 + (- .02)] / (.17 - (- .02)} / 1.17^3
P 0 = $5.50