Question

Kirksville Inc. has 1,100 bonds outstanding that are selling for $992 each. The bonds carry a 6.0 percent coupon, pay interest semi-annually, and mature in 7.5 years. The company also has 9,500 shares of 5% preferred stock at a market price of $40 per share. This month, the company paid an annual dividend in the amount of $1.20 per share. The dividend growth rate is 5.0 percent. The common stock is priced at $30 a share and there are 34,500 shares outstanding. The company is considering a project that is equally as risky as the overall company. This project has initial costs of $630,000 and operating cash flows of $80,000 a year for the next 10 years and salvage value of $20,000 at the end of 10 years. The net working capital (NWC) is expected to increase by $10,000 a year until the end of the project life. All the NWCs will be recovered when the project is completed. The project will be depreciated straight-line to zero over the project’s 10-year life. The tax rate is 21%.

1. (15 points) What is Kirksville’s weighted average cost of capital?

2. (10 points) What is the net present value (NPV) of this project? Should you accept the project? Explain why.

3. (5 points) What is the internal rate of return (IRR) of this project? Should you accept the project if you apply the IRR decision rule?

Answer 1

a). WACC calculation:

WACC = sum of weighted costs of all capital

Cost of debt (kd): FV = 1,000; PV = 992; PMT = coupon rate*par value/2 = 6%*1000/2 = 30; N = 7.5*2 = 15, CPT RATE.

Semi-annual YTM = 3.07%

Market value of debt = number of bonds*price = 1,100*992 = 1,091,200

kd = 3.07%*2 = 6.13%

Cost of preferred stock = annual dividend/current price = (5%*100)/40 = 12.5%

Market value of preferred stock (wps) = number of preferred shares*price per share = 9,500*40 = 380,000

Cost of equity (ke) = (D1/P0) + g = (1.20*(1+5%)/30) + 5% = 9.20%

Market value of common stock = number of shares*price per share = 34,500*30 = 1,035,000

Total market value of capital = 1,091,200 + 380,000 + 1,035,000 = 2,506,200

Weight of debt (wd) = market value of debt/total capital = 1,091,200/2,506,200 = 43.54%

Weight of preferred stock (wps) = market value of preferred stock/total capital = 380,000/2,506,200 = 15.16%

Weight of common stock (we) = market value of common stock/total capital = 1,035,000/2,506,200 = 41.30%

WACC = (wd*kd*(1-Tax rate)) + (wps*kps) + (we*ke)

= (43.54%*6.13%*(1-21%)) + (15.16%*12.5%) + (41.30%*9.2%) = 7.80%

b). Project NPV:

Initial cost = 630,000

FCF from Year 1 to Year 10 = OCF - Increase in NWC = 80,000 - 10,000 = 70,000

PV of all FCFs: PMT = 70,000; N = 10; rate (WACC) = 7.80%, CPT PV.

PV = 473,869.45

After-tax salvage value = salvage value*(1-Tax rate) = 20,000*(1-21%) = 15,800

PV of after-tax salvage value = 15,800/(1+7.80%)^10 = 7,452.06

Recovery of NWC at the end of the project = sum of increase in NWC over project life = 10,000*10 = 100,000

PV of recovered NWC = 100,000/(1+7.80%)^10 = 47,164.91

Project NPV = - initial cost + PV of FCFs + PV of after-tax salvage value + PV of recovered NWC

= -630,000 + 473,869.45 + 7,452.06 + 47,164.91 = - 101,513.58

The project should not be accepted as it has a negative NPV.

c). IRR = 4.46% (using IRR function)

Formula	Year (n)	0	1	2	3	4	5	6	7	8	9	10
FCF10 = FCF + Recovered NWC + After-tax salvage value	FCFs	-630,000	70,000	70,000	70,000	70,000	70,000	70,000	70,000	70,000	70,000	185,800
	IRR	4.46%

The IRR is less than the required WACC of 7.80% so the project should not be accepted.