Question

1. Your firm’s market value balance sheet is given as follows:

   Market Value Balance Sheet
   Excess cash	$30M	Debt	$230M
   Operating Assets	$500M	Equity	$300M
   Asset Value	$530M	Debt + Equity	$530M

   Assume that the you plan to keep the firm’s debt-to-equity ratio fixed. The firm’s corporate tax rate is 50%. The firm’s cost of debt is 10% and cost of equity is 20%.

   Now, suppose that you are considering a new project that will last for one year. According to your analysis, free cash flows from the project are -$1,000 today (i.e. year 0) and $1,322.40 one year from today (i.e. year 1). This new project can be viewed as a “carbon copy” of the entire firm’s existing business. You want to find the NPV of the project using three different DCF methods: WACC/APV/FTE.

   What is the firm’s WACC?

   	A.	20%
   	B.	10%
   	C.	14%
   	D.	16%

1. Under the WACC approach, the NPV of the project is obtained by discounting future ______ using the WACC.

   	A.	Tax savings
   	B.	Free cash flow to equity
   	C.	Free cash flow to debt
   	D.	Free cash flow

1. What is the NPV based on the WACC approach?

   	A.	$20
   	B.	$160
   	C.	$140
   	D.	$200

1. What is the firm’s unlevered cost of capital?

   	A.	20%
   	B.	10%
   	C.	16%
   	D.	14%

1. What is the NPV of the project if the project were financed by 100% equity (i.e. unlevered)?

   	A.	$140
   	B.	$200
   	C.	$160
   	D.	$20

1. The new project is financed with the same capital structure as the entire firm (implying that the interest tax shield should be discounted using the unlevered cost of capital). To do so, you raise $464 in debt at year 0. Then, what would the present value of the interest tax shield be? Assume that the interest rate on the debt is the same as the firm’s cost of debt (i.e. 10%).

   	A.	$200
   	B.	$140
   	C.	$20
   	D.	$160

1. What is the NPV of the project based on the APV approach?

   	A.	$160
   	B.	$20
   	C.	$140
   	D.	$200

1. What is the FCFE at year 0? (Hint: You raise $464 in debt at time 0.)

   	A.	-$536
   	B.	$835.20
   	C.	-$835.20
   	D.	$536

1. What is the FCFE at year 1? (Hint: You repay the debt of $464 at time 1.)

   	A.	-$536
   	B.	$536
   	C.	$835.20
   	D.	-$835.20

1. Which of the following serves as the discount rate for free cash flows to equity?

   	A.	16%
   	B.	14%
   	C.	20%
   	D.	10%

1. What is the NPV of the project based on the FTE approach?

   	A.	$200
   	B.	$160
   	C.	$140
   	D.	$20

1. Do the WACC/APV/FTE approaches produce identical NPV values?

   Yes

   No

Answer 1

a) WACC= weighted average of the costs of various sources of capital, i.e, Debt and equity in this case.

Cost of equity= 20%

cost of debt= 10% (we are assuming that 10% is the post-tax cost of debt since the Question mentions 'Firm's cost of debt')

Sources	Amount	Cost(%)	Weights	Cost*Weights
Equity	300	20	300/530= 0.566	20*0.566= 11.32
Debt	230	10	230/530= 0.434	10*0.434=4.34
TOTAL	530			15.66

Hence, WACC= 15.66% = 16% (rounding off to the nearest %): Option D

b) Answer: Option D) Free Cash Flow (to the Firm) Reasons are numerated below:

1) The question mentions that the new project can be viewed as a “carbon copy” of the entire firm’s existing business, meaning that the project will be funded by both debt and equity.

2) Also, WACC is used as a discounting rate only for Free Cash Flows to the Firm. For Free Cash Flows to Debt, we would use Cost of debt (10%) and for Free Cash Flows to Equity, we would use Cost of Equity (20%).

c) NPV based on WACC approach: option C

NPV= PV of cash inflows- PV of cash outflows= 1322.4* discounting factor (16%, 1yr) - 1000
= $139.90= $ 140 (rounding off to nearest ruppee)

d) Firm's unlevered cost of capital: This refers to the cost of capital used for evaluating a project which has no debt involved in funding.

In this case, the unlevered cost of capital will be equal to the cost of equity= 20%

hence, option A