Question

[Q24-35] 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 NPV of the project based on the FTE approach?

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

Answer 1

A. WACC METHOD

CALCULATION OF WACC
Kd=	cost of debt* (1-tax rate)
	.10*(1-.50)
	0.05
Debt Proportion	230/530
	0.434
Ke=	0.20
Equity Proportion	300/530
	0.566
WACC=	(0.05*0.434)+(.20*0.566)
	0.1349
	13.49%

CALCULATION OF NPV USING WACC METHOD

Year	Cash flows	Discounting factor @ 13.49%	Discounting Cash flows
0	-1000	1	-1000
1	1322.40	0.8811	1165.17
		NPV	165.17

B. APV METHOD

NPV under APV method= NPV (to an unlevered firm)+ NPVF (including financing effects)

Cost of equity (Ke)= 20%

Year	Cash flows	Discounting factor @ 20%	Discounting Cash flows
0	-1000	1	-1000
1	1322.40	0.833	1101.56
		NPV (unlevered firm)	101.56

Debt value of $230 @ 10% and the tax rate is 50%.

Therefore, interest tax shield= $230*10%*50%

=$11.5

NPVF (financing side effects)= (11.5/1.10)

= $10.45

NPV CALCULATION UNDER APV METHOD= NPV+NPVF

= $101.56+ $10.45

= $112.01

C. FTE METHOD

FTE method involves discounting the levered cash flows at the levered cost of equity.

1. Calculation of levered cash flows

Since, the company is using debt component of $230, the equity shareholders have to bring in $770 to finance the full cash outflow of $1000 today i.e. Year 0.

Firstly we will calculate after tax cost of interest = $230* 0.10* (1-0.50)= $11.50

Cash flow for year 1= $1322.40- $11.50- $230= $1080.90

2. Calculation of cost of equity

Value of the project= (1322.40/1.20)+10.45= $1112.01

When value of the project is $1112.01, the debt value is $230. Therefore, the equity component will be= $1112.01-$230 = $882.01

Cost of equity= .20+ (230/882.01)(1-0.50)(0.20-0.10)

= 0.2130= 21.30%

3. Discounting the levered cash flows at 21.30%

Year	Cash flows	Discounting factor @ 21.30%	Discounting Cash flows
0	-770	1	-770
1	1080.90	0.824	890.66
		NPV	120.66