Question

A firm is considering investing in a new project. According to its cost of capital while using debt, preferred stock and new common stock, the project is expected to have an initial after-tax cost of $5,000,000. Furthermore, the project is expected to provide after-tax operating cash flows of $1,800,000 in year 1, $2,900,000 in year 2, $2,700,000 in year 3 and $2,300,000 in year 4.

A firm has determined its optimal capital structure, which is composed of the following sources and target market value proportions.

Source of Capital	Target Market Proportions
Long-term debt	40%
Preferred stock	10%
Common stock equity	50%

Debt: The firm can raise debt by selling 15-year, $1,000 par value, 9% coupon interest rate bonds that pay annual interest. A flotation cost of 4 percent of the face value would be required in addition to the premium of $10.

Preferred Stock: Preferred stock, regardless of the amount sold, can be issued with an $80 par value and a 12% annual dividend rate. The cost of issuing and selling the stock is $3 per share.

Common Stock: The firm’s common stock is currently selling for $10 per share. The dividend that was paid last year was $0.87. Its dividend payments have been growing at a constant rate of 5% per year. It is expected that to attract buyers, a new common stock issue must be underpriced $2 per share, and the firm must also pay $1 per share in flotation costs.

Retained Earnings: A corporation expects to have earnings available to common shareholders (net income) of $1,000,000 in the coming year. The firm plans to pay 40 percent of earnings available in cash dividends. The retained earnings have been already exhausted. Therefore, the firm will use new common stock as the form of common equity financing. Additionally, the firm’s marginal tax rate is 40 percent.

Maximum acceptable payback period of this project is 3 years. Calculate the payback period for this project.

Calculate the project’s NPV.

Calculate the project’s IRR.

Should the firm make the investment? Why?

Answer 1

	CALCULATION OF COST OF CAPITAL:
1]	Before tax cost of debt = YTM
	YTM using a online calculator = 9.38%.
	[Inputs for YTM are, Price = 1000+10-40 = 970;
	Coupon = 9%, Frequency = Annual, Years = 15]
	After tax cost of debt = YTM*(1-t) = 9.38%*(1-40%) =	5.63%
2]	Cost of preferred stock = Preferred dividend/Price = 80*12%/(80-3) =	12.47%
3]	Cost of new equity using constant dividend growth model = Next expected dividend/(Price-discount-Flotation cost)+Growth rate = 0.87*1.05/(10-2+1)+0.05=	15.15%
4]	WACC = 5.63%*40%+12.47%*10%+15.15%*50% =	11.07%
a]	Year	Cash flow	Cumulative Cash Flow
	0	$ -50,00,000	$ -50,00,000
	1	$      18,00,000	$ -32,00,000
	2	$      29,00,000	$ -3,00,000
	3	$      27,00,000	$ 24,00,000
	4	$      23,00,000	$      47,00,000
	Payback period = 2+300000/2700000 =	2.11	Years
b]	Year	Cash flow	PVIF at 11.07%	PV at 11.07%
	0	$ -50,00,000	1	$ -50,00,000
	1	$      18,00,000	0.90090	$       16,21,622
	2	$      29,00,000	0.81162	$       23,53,705
	3	$      27,00,000	0.73119	$       19,74,217
	4	$      23,00,000	0.65873	$       15,15,081
	NPV			$       24,64,625
c]	IRR is that discount rate for which NPV = 0. It has to be found out by trial and error by discounting
	the cash flows at various interest rates till 0 NPV is got.
	Year	Cash flow	PVIF at 32%	PV at 32%	PVIF at 31%	PV at 31%
	0	$ -50,00,000	1	$ -50,00,000	1	$ -50,00,000
	1	$      18,00,000	0.75758	$       13,63,636	0.76336	$      13,74,046
	2	$      29,00,000	0.57392	$       16,64,371	0.58272	$      16,89,878
	3	$      27,00,000	0.43479	$       11,73,929	0.44482	$      12,01,019
	4	$      23,00,000	0.32939	$         7,57,586	0.33956	$        7,80,985
	NPV			$           -40,477		$ 45,928
	0 NPV is got between discount rates of 31% and 32%.
	By simple interpolation, IRR = 31%+1%*45928/(45928+40477) =	31.53%
d]	The investment should be made as:
	*The payback perioid is less than the maximum acceptable payback period.
	*NPV is positive [because of which IRR>WACC]