Question

Blue Angel, Inc., a private firm in the holiday gift industry, is considering a new project. The company currently has a target debt–equity ratio of .45, but the industry target debt–equity ratio is .40. The industry average beta is 1.30. The market risk premium is 7 percent, and the risk-free rate is 5 percent. Assume all companies in this industry can issue debt at the risk-free rate. The corporate tax rate is 34 percent. The project requires an initial outlay of $688,000 and is expected to result in a $108,000 cash inflow at the end of the first year. The project will be financed at the company’s target debt–equity ratio. Annual cash flows from the project will grow at a constant rate of 5 percent until the end of the fifth year and remain constant forever thereafter.

      

Calculate the NPV of the project. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

    

NPV

$

Answer 1

Industry levered beta=1.3, Industry debt-equity ratio=0.4, tax rate=0.34
Industry unlevered beta = Industry levered beta/{1+[(1-tax rate)*Industry debt-equity ratio]} = 1.3/{1+[(1-0.34)*0.4]} = 1.3/{1+[0.66*0.4]} = 1.3/(1+0.264) = 1.3/1.264 = 1.03

Blue angel debt-equity ratio=0.45
Blue angel beta = Industry unlevered beta*{1+[(1-tax rate)*Blue angel debt-equity ratio]} = 1.03*{1+[(1-0.34)*0.45]} = 1.03*{1+(0.66*0.45)} = 1.03*(1+0.297) = 1.03*1.297 = 1.34

Blue angel required return (r) = risk free rate+(Blue angel beta*Market risk premium) = 5%+(1.34*7%) = 5%+9.38% = 14.38%

Terminal cashflow from the project at the end of 5th year = [Annual cashflow*(1+growth rate)^4]/r = [108000*(1+0.05)^4]/0.1438 = [108000*(1.05^4)]/0.1438 = (108000*1.2155)/0.1438 = $912,897.60

Computation of NPV of the project:

Year	Type	Cashflow	PVF @ r	NPV
0	Initial outlay	-$688,000	1.00	-$688,000.00
1	Annual cashflow	$108,000	1/1.1438 = 0.8743	$94,424.40
2	Annual cashflow	108000*1.05 = $113,400	0.8743/1.1438 = 0.7644	$86,682.96
3	Annual cashflow	113400*1.05 = $119,070	0.7644/1.1438 = 0.6683	$79,574.48
4	Annual cashflow	119070*1.05 = $125,023.50	0.6683/1.1438 = 0.5843	$73,051.23
5	Annual cashflow+ Terminal cashflow	(125023.5*1.05)+912897.6 = $1,044,172.28	0.5843/1.1438 = 0.5108	$533,363.20
				$179,096.27