Question

A real estate development firm is looking to invest in a new apartment complex that requires an initial investment of $8 million today. This project will yield free cash flows of $1 million each year for the next 15 years (from t=1 to t=15). The firm is financed half with equity and half with bonds (assume no cash). The firm's beta is 1.5, the yield to maturity on its debt is 6.0%, and its tax rate is 20%. If the expected return on the S&P500 Index is 7.0% and the risk-free rate is 1.0%, what is the NPV of this project (in millions)?

A) $4.67 million

B) -$1.12 million

C) 0

D) $.88 million

E) 1.75 million

Answer 1

First of all, we shall calculate weighted average cost of capital, Discount rate to be used for NPV calculation.
Cost of debt
Yiled to maturity (Pretax cost of debt)=				6% or	0.06
Tax rate =				20% or	0.2
After tax cost of Debt = Pretax cost of debt * (1-tax rate)
		0.06 * (1-0.20)
		0.0480
After tax cost of debt is 0.0480 or 4.80%
Cost of equity
Risk free rate of return				1%
Beta				1.5
Marekt rate of return				7%
Cost of equity = Risk free rate + Beta * (market rate of return - risk free rate of return)
	1% + 1.5 * (7%-1%)
10% or	0.1000
Cost of capital
Weight of Debt =		0.5
Weight of Euity =		0.5
Weighted average cost of capital = (Weight of equity * cost of equity) + (Weight of Debt * Cost of debt)
	(0.50 * 0.10) + (0.50* 0.0480)
	0.0740
So, WACC or Required return is 0.0740 or 7.40%
Calculation of NPV
Initial investment at Year 0					$     -8.00	Millions
Annual free cash flow			1	Millions
Cumulative P.V.F. @7.4% for 15 Years
(1-(1/(1+0.074)^15))/0.074			8.882201
Present value of Annual cash flows					$       8.88	millions
(1million * 8.882201)
					_________
Net present value					$       0.88	millions
					_________
So, Answer is D, NPV of project is $0.88 millions