MIDTERM Word Problems Flashcards
Part II Short Answers (50 points) – each question is worth 10 points. Please answer Part II directly on the exam paper. You may use blank paper at the end of the test if needed.
Question 1: Capital Budgeting Methods
Suppose a company has the following information on six independent projects:
a. (3 pts) Which projects should the company undertake if it has no capital constraints? Briefly explain
b. (3 pts) What is the impact on the company’s shareholder value in (b)? c. (2 pts)
c.Which projects should the company undertake if it has a capital constraint of $15 million? Briefly explain.
d. (2 pts) What is the loss to the company from the capital rationing constraint in (d)?
a. (3 pts) Which projects should the company undertake if it has no capital constraints? Briefly explain.
If the company had no capital constraints it would undertake the Project’s B, D, E, and F. This is because for all these projects the internal rate of return is greater then the cost of capital K the discount rate. If it is greater then the project’s cash flows are generating more then what it cost to finance the project, leading to a positive NPV. Projects A, and C should not be taken as it’s IRR less then the cost of capital, adding no value and leading towards a negative NPV
b. (3 pts) What is the impact on the company’s shareholder value in (b)? c. (2 pts)
NPV Project B = -8,000,000 + 3,000,000 1-(1+0.15)-40.15 = 564,935.08
NPV Project D = -5,000,000 + 1,600,000 1-(1+0.08)-40.08 = 299,402.94
NPV Project E = -4,000,000 + 1,800,000 1-(1+0.14)-30.14 = 178,937.64
NPV Project F = -6,000,000 + 1,500,000 1-(1+0.07)-50.07 = 150,296.15
The impact on the shareholder value by going forward with this project is increasing NPV with this combined NPV value of $1,193,571.83
c.Which projects should the company undertake if it has a capital constraint of $15 million? Briefly explain.
If it has a capital constraints of 15 million, the company should undertake the projects with the highest NPV value only which is project B and D. This will have a combined NPV of 564,935.08 + 299,402.94 = 864338.03
d. (2 pts) What is the loss to the company from the capital rationing constraint in (d)?
The loss of the company is the forgone value of not going ahead with projects E and F which total to 178,937.64 + 150,296.15 = 329,233.80
As CEO of MNOP Inc. you are considering selling the firm and want to know what it is worth. You approximate next years EBIT to equal $60 million, declining at a rate of 2.5% per year (forever) as competitors introduce superior offerings. Your firm has a target D/V ratio of 40% and has no capital expenditures or working capital to worry about. Expected borrowing cost is 5%, tax rate is 22%, treasury bond yield is 3%, and the market risk premium is 5%. Using the information provided and the table below, what is the value of MNOP Inc.?
Unlevered Equity Betas to get Asset Beta
βAsset = βequity1+(1-t)*B
Given:
βequity Firm A = 2.25, βequity Firm B = 1.75
D/V - Debt to value indeed to convert to D/E as the B = D/E in asset beta formula
Firm A Conversion: D/V = 0.40 D/E = 0.45/1-0.45 = 0.818
Firm B Conversion: D/V = 0.20 D/E = 0.20/1-0.20 = 0.25
For Firm A:
βAsset = βequity1+(1-t)D/E
= 2.251+(1-0.22)0.818 = 2.251.63804 =1.37
For Firm B:
βAsset = βequity1+(1-t)D/E
= 1.751+(1-0.22)0.25 = 1.751.195 = 1.46
Find the Average Beta Calculation
βassetfirm =1.37 + 1.462 = 1.415
RELEVERAGE the beta for the firm (MNOP Inc)
Firm has a target D/V ratio: 40% = 0.40
Convert D/V ratio into D/E: D/V = 0.40 D/E = 0.40/1-0.40 = 0.666
βequityFirm = βassetavg * ( 1 + (1-Tc) * β)
βequityFirm = 2.83 * ( 1 + (1-0.22) * 0.667)
βequityFirm = 1.415 * ( 1 + (1-0.22) * 0.667)
βequityFirm = 1.415 * ( 1 + (1-0.22) * 0.667) = 2.15
Estimate Cost of Equity
Using CAPM: market risk premium = 5%, rf = treasury bond yield
CAPM:
Cost of Equity = Rf +βe * ) *([ E[Rm] - Rf])
Cost of Equity = 3% + 2.15 * (5%) = 13.75%
Calculate WACC
WACC = E/V * Cost of Equity + D/V * Cost of Debt * (1-t)
D/V = target : 0.40
E/V = 1- 0.40 = 0.60
Cost of Equity = 15.065%
Cost of Debt = 5%
WACC = 0.60 * 13.75% + 0.40 * 5% ( 1- 0.22) = 9.81%
- Value of Firm = EBIT (1- t)WACC - g
Value of Firm = 60(1-0.22) / 0.0981 - (- 0.025) = 380 million
Question 3: Cost of Capital PQRST Corp. can issue new 15-year bonds at par that pay a 6.8% annual coupon, new preferred shares that pay a $5 annual dividend (market price for the firm’s preferred shares is currently 16 times the dividend). The firm’s 1,000,000 common shares currently pay an annual dividend of $2.65 which has grown at a compound rate of 4% each year. The firm’s share price is $60, the broad market is only expected to return 6% this year while government T-Bills are paying a rate of just 1%. The firm’s average tax rate is 30%. Assuming a market beta of 1.45 for PQRST Corp. and a target capital structure of 35% debt, 15% preferred and 50% common equity, estimate the firm’s cost of capital.
Given:
15 year bond at par
6.8% annual coupon
$5 dividend, market price for preferred shares = $80
1,000,000 common shares pay dividend of 2.65 , growing 4% each
Firms share price
Estimate the Cost of Debt
rb(1-Tc), where rb = YTM = 6.8% , tax = 30%
0.068(1-0.30) = 4.76%
Estimate the Cost of Equity - Preferred
Cost of Equity = d1/price = $5 / ($5 * 16) = 0.0625 = 6.25%
Estimate Cost of Equity - Common (Two Ways - DDM, CAPM)
Using CAPM:
Ke = rf + βe * (E[rm] - rf)
Ke = 1% + 1.45 * [ 6% - 1%]
Ke = 8.25 %
Using DDM
Re =D1p0 + g
Calculating D1: D1 = D0(1+g) = 2.65 ( 1+ 0.04) = 2.756
Re = 2.75660 + 0.04 = 0.08593 = 8.593%
Average - Cost of Equity Common
Re = 8.593% + 8.25% / 2 = 8.42%
Determine the weights of debt and equity and calculate WACC
WACC = =wD⋅rD+wP⋅rP+wE⋅rE
wD = weight of debt = 35%
wP= weight of preferred equity = 15%
wE = weight of common equity = 50%
rD = cost of debt = 4.76%
rP = cost of preferred equity = 6.25%
rE = average cost of equity = 8.42%
WACC= 0.35× 4.76% +0.15×6.25%+0.50×8.42% = 6.81
Dania Incorporated is considering purchasing a new machine that costs $900,000. The machine will have a salvage value of $150,000 at the end of 5 years when it is sold. There will be an initial working capital requirement of $40,000 that will be recovered at the end of the project. The CCA rate on the machine is 30%, the corporate tax rate is 35%, and the discount rate is 15%. What is the net present value of the investment if the project is expected to generate the following pre-tax cash flows
Initial Investment = 900,000 + 40,000 = 940,000
NPV = -initial investment + PV CCA Tax Shield +PV of After tax cash flow + PV Salvage + PV Working
PV CCA Tax Shields = C * d * T k + d *1 + 1.5k 1 + k -SV * d T k + d1 (1+k)n
= 900,000 * 0.30 * 0.35 0.15 + 0.30 *(1-1 + 1.5(0.15) 1 + 0.155) -150,000 * 0.30 *0.35 0.15+0.30 *(1+0.15)5
= 210,000 * 0.391 - (15750 / 0.9051)
= 210,0000.391 - 17401 = ???
PV of Salvage Value = 150,0001.155 = 74,576.51
PV AFTER TAX Cash Flows: (1-0.35) = 0.65
Cash Flows after Tax:
Year 1: 250,0000.65 = 165,000 PV = 165,000 / (1.15)^1 = 141,304
Year 2: 350,000 * 0.65 = 227,500 PV = 227,500 / (1.15)^2 = 171,984
Year 3: 400,000 * 0.65 = 260,000 PV = 260,000/1.15^3 = 170,863
Year 4: 400,000 * 0.65 = 260,000 PV = 260,000/1.15^3 = 148,645
Year 5: 500,000 * 0.65 = 325,000 PV = 325,000 / 1.15^4 = 161, 724
TOTAL PV AFTER TAX CF SUM = 794,520
PV WC = 40,000 1.155 = 19,887
Question 5: Breakeven Analysis A start-up EV company wants to build a niche line of vehicles and is looking into building a small manufacturing plant. The plant will cost $1,000,000 to build. The PV of the CCA tax shield is $150,000. The fixed costs to run the plant are $75,000 year. Each vehicle costs $60,000 to build and is expected to sell for $100,000. The project will last 10 years. The company has a tax rate of 26% and a WACC of 8%. How many cars need to be sold each year for the project to break even?
Use the NPV to solve
NPV = -C + + PV(Tax Sheild) + (Selling Price - Variable Costs)* Q + Fixed Costs) * PVIFA
In order to solve NPV set NPV = 0
NPV = -1,000,000 + 150,000 + (100,000 - 60,000) * Q - 75,000)(1-Tr) * PVIFA(10YEARS,8%)
NPV = -1,000,000 + 150,000 + (100,000 - 60,000) * Q - 75,000)(1-0.26) * (1-(1+k)-nk)
NPV = - 1,000,000 + 150,000 + (100,000 - 60,000) * Q - 75,000) *(0.74) (1-(1+0.08)-100.08)
0 = -1,000,000 + 150,000 + (40,000Q - 75,000) 0.74 6.71008
0 = -1,000,000 + 150,000 + (40,000Q - 75,000) *4.96545
0 = -1,000,000 + 150,000 + (40,000Q - 75,000) *4.96545
0 = -1,000,000 + 150,000 + 198,618Q - 372,408
Q = 6.15
A company is considering the purchase of a new machine priced at $300,000 to replace an existing machine. The market value of the existing machine is $100,000 and its expected salvage value is $10,000 at the end of 8 years. The company will benefit from the new machine by reducing annual operating expenses by $50,000 over the life of the project. The new machine will have a salvage value of $50,000 at the end of 8 years. The firm’s marginal tax rate is 30% and its marginal cost of capital is 10%. Both machines have a CCA rate of 40% and the CCA class will remain open. Assume 150% first-year deduction in the first year.
a) (2 points) What is the present value of operating expenses savings over the life of the project?
b) What is the present value of the net change in CCA tax shield?
c) (2 points) Calculate the NPV of the replacement. Should the company replace the machine? For full marks, clearly state YES or NO.
d) For each of the inputs below, state whether the indicated change will increase or decrease the breakeven sales volume. For example, if you believe that an increase in the CCA rate leads to an increase in the NPV of the replacement, circle “Increase.” You do not need to explain the answer.
a) (2 points) What is the present value of operating expenses savings over the life of the project?
Operating expenses = 50,000
Time = 8 years
Cost of Capital = 10%
PV = 50,000(1-0.30)(1-(1+0.10)-80.10) =186,722.41
Apply the (1 - tax rate) when the savings (or any benefit) you’re calculating are subject to taxes. In this case, the operating expense savings reduce the company’s taxable income
b) What is the present value of the net change in CCA tax shield?
PV△ CCA Tax Shield = C d T k + d 1 + 1.5k1 + k -SV d Tk + d 1(1+k)n
C = 300,000 - 100,000 = 200,000
d = 0.40 (basically CCA)
T = 30%
k = 10%
Salvage Value Net Change = 50,000 - 10,000 = 40,000
PV△ CCA Tax Shield = 200000 0.40 0.30 0.10 + 0.40 1 + 1.5(0.10)1 + 0.10 -40,000 0.40 0.300.10 + 0.40 1(1+0.10)8
PV△ CCA Tax Shield = 48,000 1.045454545 - 9,000 0.466507380
PV△ CCA Tax Shield = 45, 983.25
c) (2 points) Calculate the NPV of the replacement. Should the company replace the machine? For full marks, clearly state YES or NO.
NPV = - C + PV(Salvage Value) + PV(CCA Tax Shield) + PV(Operating Expenses)
NPV = -200,000 +40000(1.1)8+ 45,983.25 + 186, 722.41
NPV = 51, 365.95
NPV > 0, positive, Yes should replace
d) For each of the inputs below, state whether the indicated change will increase or decrease the breakeven sales volume. For example, if you believe that an increase in the CCA rate leads to an increase in the NPV of the replacement, circle “Increase.” You do not need to explain the answer.
Change to Input Breakeven sales volume will: (Circle one of the three choices below.)
CCA rate rises: Breakeven sales volume will: Increase / Decrease / Not change
Tax rate rises Breakeven sales volume will: Increase / Decrease / Not change
New machine price at t=0 rises Breakeven sales volume will: Increase / Decrease / Not change
Cost of capital rises: Breakeven sales volume will: Increase / Decrease / Not change
(More depreciation reduces taxable income, increasing tax savings, fewer sales to break even
Higher tax rate increases the value of the tax shield from depreciation.
A higher machine cost means higher fixed costs to recover.
Higher cost of capital means future cash flows are worth less today)
S2. (10 points) You have two firms (A and B) that operate in the same industry and sell their products for $15. Fixed costs of firm A are $1000 and variable costs are $10 per unit. The depreciation of firm A is $250. Fixed costs of firm B are $2000 and variable costs are $5 per unit. The depreciation of firm B is $500.
a) (3 points) What are the accounting break-even production quantities of these firms?
b) (4 points) Which of the firms’ operation is riskier in your opinion? Explain your answer.
(3 points) All else equal, which firms’ shareholders will demand a higher rate of return? Explain your answer using equations in the formula sheet.
a) (3 points) What are the accounting break-even production quantities of these firms?
Q = FC + DP - C
Firm A: Q = 1000 + 25015 - 10= 250
Firm B: Q = 2000 + 50015 - 5 = 250
b) (4 points) Which of the firms’ operation is riskier in your opinion? Explain your answer.
Firm B is riskier as they have higher fixed costs to recover. High fixed costs amplify earning fluctuations, due to them having higher operating leverage because of higher beta. Firms that can quickly adjust costs based on sales are less risky, based on their low operating leverage due to having a lower beta.
For Firm A: fixed costs are 1000: 1000/10 = 100
For firm B: fixed costs are 2000: 2000/5 = 400
(3 points) All else equal, which firms’ shareholders will demand a higher rate of return? Explain your answer using equations in the formula sheet.
Firm B has higher beta due to high operating leverage. Firm A has lower asset beta due to low operating leverage. Firm B has high leverage which will increase equity beta, raising the required rate on equity because more debt raises risk. Firm B will demand a higher rate.
S3. (10 points) It is March 2024, and you are thinking whether to give up on your Rotman Commerce degree and become an entrepreneur. You know that first of all, you need to conduct research of potential ideas and it costs $9,500,000. There is a 50% chance you will come up with a good idea and a 50% chance that you will end up with nothing (i.e., zero NPV), wasting one year of your life, and dropping out of school. In the event you manage to come up with a good idea, you need to invest $2,000,000 in capital in March 2025, then the product will be launched in March 2026. In March 2026, there is a 30% probability that another firm will emerge as a competitor, in which case the resulting annual cash flows will become $1,000,000, in perpetuity, starting March 2026. Alternatively, there is a 70% chance that you will have a monopoly, leading to annual cash flows of $3,000,000, in perpetuity, starting March 2026. The discount rate is 10%
a) (4 points) Suppose that you have successfully come up with a good idea after conducting research. Will you invest $2,000,000 in March 2025?
b) (2 points) In March 2024, would you conduct research of potential ideas?
c) (4 points) Assume that you have the option to sell your firm’s intellectual property (i.e., business model) in March 2026 to a competitor for $20 million without receiving any cash flows. What is the value of this real option in March 2024?
a) (4 points) Suppose that you have successfully come up with a good idea after conducting research. Will you invest $2,000,000 in March 2025?
Conduct Research Cost: 9,500,000
Discount Rate = 10%
Good Idea: 50% Chance
Invest 2,000,000 in capital in March 2025 then launch product in March 2026
March 2026: 30% probability firm comes as competitor, annual cash flows are 1,000,000, 70% monopoly, annual cash flows 3,000,000 in perpetuity starting March 2026
Bad Idea: 50% Chance
Zero NPV
NPV = (-2,000,000 + 0.30(1,000,0000.10) + 0.70(3,000,0000.10) =22,000,000
b) (2 points) In March 2024, would you conduct research of potential ideas?
March 2024:
Cost: 9,500,000
50% good idea - NPV of that good idea is
50% nothing: zero NPV
NPV = -9,500,000 + 0.50 (22,000,0001.1) + 0.50(0) = 500,000
NPV is positive, conduct
c) (4 points) Assume that you have the option to sell your firm’s intellectual property (i.e., business model) in March 2026 to a competitor for $20 million without receiving any cash flows. What is the value of this real option in March 2024?
Value of real Option is difference between NPV with and without the option to sell firm to competitor
Option to sell to a competitor for 20 million in March 2026:
NPV = -2,000,000 + 0.30(20,000,0001.1) + 0.70(3,000,0000.10) = 24,454,545.45
Option to not sell to a competitor: (basically 2024)
NPV(2024) = -9,500,000 + 0.5(24,454,545.451.1 )+ 0.5(0)
NPV(2024) = 1, 615, 702. 477
VALUE of Option = NPV with Selling - NPV without selling
Value of Option = 1,614,702.477 -500,000 = 1,114,702.477
