TVM (Retirement, Education, Mortgage)

Question 1

Jennifer and Ben have a four-year-old son, Danny. They want to start saving for Danny’s college education. They expect Danny to attend college for four years starting on his 18th birthday. The current cost of college education is $50,000 a year. It is expected that the cost of attending college will increase by 10 percent each year. Assuming they can earn a 12 percent return on their investments, how much do they need today to fund Danny’s education at age 18?

$151,295
$200,000
$208,862
There is not enough information provided to answer this question.

Answer 1

Solution: The correct answer is A.

$0 CF

0 CF

13 Nj

50,000 CF

4 Nj

((1.12/1.1) -1)*100 = I/YR

NPV = $151,295.28

Question 2

Joe wants to retire in 20 years when he turns 70. Joe wants to have enough money to replace 75% of his current income less what he expects to receive from Social Security at the beginning of each year. His Social Security benefit is $20,000 per year in today’s dollars at his normal age retirement of age 67. However, he will begin collecting Social Security benefits when he retires. Joe is conservative and wants to assume a 7% annual investment rate of return and assumes that inflation will be 3% per year. Based on his family history, Joe expects that he will live to be 95 years old. Joe currently earns $100,000 per year and he expects his raises to equal the inflation rate. He has accumulated $199,571 towards retirement. How much does he need to save every year to fulfill his retirement goals?

$16,142
$17,500
$19,486
$20,975

Answer 2

Solution: The correct answer is B.

The answer is calculated as follows:

*Social Security must be increased by 24% to account for delayed benefits at 8% per year, for the 3 years he delayed benefits.

Step 1:  Determine amount to be funded
Income today		$100,000.00
WRR		75%
Needs		$75,000.00
Less Social Security* & Pension	$(24,800.00)
Amount to be funded	$50,200.00

Step 2: Inflate funds to retirement age
PV		$(50,200.00)
N		20
i		3.00%
Pmt		0
FV		$90,666.78

Step 3:  PV of retirement annuity (BEG mode)
PMT		$90,666.78
N		25
i		3.8835%
FV		-  
PV		($1,489,697.78)

Step 4:  Annual funding amount	(END Mode)
FV		$1,489,697.78
N		20
I		7.00%
PV		($199,571)
Pmt		($17,500.00)

Question 3

Barbara Reed owns an LMN, Inc. bond with a par value of $1,000. LMN is a AA-rated bond that matures in 7 years. Barbara receives $55 of interest income from LMN semiannually. Comparable debt, i.e., is AA-rated, 7-year maturity, yields 12%. The bond’s duration is 5 years. What is the intrinsic value of the bond?

$703.36
$880.80
$953.53
$954.36

Answer 3

Solution: The correct answer is C.

The intrinsic value of a bond is its calculated present value.

N = 7 × 2

i = 12 ÷ 2

PV = ?

PMT = 55 ($110 ÷ 2)

FV = 1,000

Question 4

Mary Grabowski owns an LMN, Inc. bond with a par value of $1,000. LMN is a AA-rated bond that matures in 7 years. Mary receives $55 of interest income from LMN semi-annually. Comparable debt, i.e., is AA-rated, 7-year maturity, yields 12%. The bond’s duration is 5 years. If the bond’s current price is $920, what is the yield to maturity of the bond?

6. 98%
7. 95%
8. 76%
9. 98%

Answer 4

Solution: The correct answer is C.

N = 7 × 2

i = ?

PV = <920>

PMT = 55

FV = 1,000

After solving for i, be sure to multiply your answer by 2 since it’s semi-annual compounding.