Question

0. Firm XYZ has 2.5 million outstanding stocks, each selling for $14 per share. The firm’s debt is publicly trading at 85 percent of its $7.5 million face value. The firm pays a 4.7% rate of interest on its new debt and has a beta of 1.8. The corporate tax rate is 40%. Assume that the risk premium on the market is 5% and that the current Treasury bill rate is 2%.

   1. a) Compute WACC

   2. b) Consider project A: the project costs 4 million and will generate after‐tax (year‐end) cash flows of $0.80 million for 4 years. The project has the same risk as the overall firm. Should the project be accepted?

   3. c) Consider now project B: the project costs 1 million and will generate after‐tax (year‐end) cash flows of $0.20 million for 8 years. Note that this project presents no risks. Should the project be accepted?

   4. d) Consider finally project C: the project costs 12.5 million and will generate after‐tax (year‐end) cash flows of $1.5 million for 8 years. The project is less risky than the overall firm, and hence has a beta of 0.7. Should the project be accepted?

Answer 1

market value of equity	2500000*14	35000000
market value of bond	7500000*85%	6375000
cost of debt = interest payment/current market price	(7500000*4.7%)/6375000	5.53%
after tax cost of debt	5.53*(1-.4)	3.32
cost of common stock	risk free rate+(market risk premium)*beta	2+(5)*1.8	11
WACC
source	market value	weight	component cost	weight*component cost
debt	6375000	0.15407855	3.32	0.5115408
common stock	35000000	0.84592145	11	9.305136
total market value	41375000
WACC =sum of weight*component cost				9.82
Project A
Year	cash flow	present value factor =1/(1+r)^n r =9.92%	present value of cash flow = cash flow*present value factor
0	-4	1	-4
1	0.8	0.910580951	0.728464761
2	0.8	0.829157668	0.663326134
3	0.8	0.755015177	0.604012142
4	0.8	0.687502438	0.55000195
NPV = sum of present value of cash flow	IRR(C1406:C1410)		-1.454195013
Project should not be considered as NPV is negative
Project C
market value of equity	2500000*14	35000000
market value of bond	7500000*85%	6375000
cost of debt = interest payment/current market price	(7500000*4.7%)/6375000	5.53%
after tax cost of debt	5.53*(1-.4)	3.32
cost of common stock	risk free rate+(market risk premium)*beta	2+(5)*.7	5.5
WACC
source	market value	weight	component cost	weight*component cost
debt	6375000	0.15407855	3.32	0.5115408
common stock	35000000	0.84592145	5.5	4.652568
total market value	41375000
WACC =sum of weight*component cost				5.16
Project C
Year	cash flow	present value factor =1/(1+r)^n r =5.16%	present value of cash flow = cash flow*present value factor
0	-12.5	1	-12.5
1	1.5	0.950931913	1.42639787
2	1.5	0.904271504	1.356407256
3	1.5	0.859900631	1.289850947
4	1.5	0.817706952	1.226560429
5	1.5	0.777583637	1.166375455
6	1.5	0.739429095	1.109143643
7	1.5	0.703146724	1.054720087
8	1.5	0.66864466	1.00296699
NPV = sum of present value of cash flow			-2.867577325
Project should not be considered as NPV is negative
Project B
market value of equity	2500000*14	35000000
market value of bond	7500000*85%	6375000
cost of debt = interest payment/current market price	(7500000*4.7%)/6375000	5.53%
after tax cost of debt	5.53*(1-.4)	3.32
cost of common stock	risk free rate+(market risk premium)*beta	2+(5)*0	2
WACC
source	market value	weight	component cost	weight*component cost
debt	6375000	0.15407855	3.32	0.5115408
common stock	35000000	0.84592145	2	1.6918429
total market value	41375000
WACC =sum of weight*component cost				2.20
Project C
Year	cash flow	present value factor =1/(1+r)^n r =2.2%	present value of cash flow = cash flow*present value factor
0	-1	1	-1
1	0.2	0.978473581	0.195694716
2	0.2	0.957410549	0.19148211
3	0.2	0.936800929	0.187360186
4	0.2	0.91663496	0.183326992
5	0.2	0.896903092	0.179380618
6	0.2	0.87759598	0.175519196
7	0.2	0.858704481	0.171740896
8	0.2	0.840219649	0.16804393
NPV = sum of present value of cash flow			0.452548644
Project should be considered as NPV is positive