Question

Here is the information that William has accumulated so far:

The Capital Budgeting Projects

He must choose one of the four capital budgeting projects listed below:  

Table 1

t	A	B	C	D
0	(19,000,000)	(20,000,000)	(18,900,000)	(19,500,000)
1	5,200,000	5,700,000	6,080,000	6,600,000
2	8,300,000	8,000,000	6,080,000	8,100,000
3	6,100,000	6,300,000	6,080,000	6,100,000
4	6,100,000	4,400,000	6,080,000	6,100,000
Risk	High	Average	Low	Average

Table 1 shows the expected after-tax operating cash flows for each project. All projects are expected to have a 4 year life. The projects differ in size (the cost of the initial investment), and their cash flow patterns are different. They also differ in risk as indicated in the above table.

The capital budget is $22 million and the projects are mutually exclusive.

Capital Structures

Grand Island Hotel has the following capital structure, which is considered to be optimal:

Debt	45%
Preferred Equity	5%
Common Equity	50%
	100%

   

Cost of Capital

William knows that in order to evaluate the projects he will have to determine the cost of capital for each of them. He has been given the following data, which he believes will be relevant to his task.

(1)The firm’s tax rate is 38%.

(2) Grand Island Hotel has issued a 9% semi-annual coupon bond with 15 years term to maturity. The current trading price is $960.

(3) The firm has issued some preferred stock which pays an annual 8.5% dividend of $100 par value, and the current market price is $98.

(4) The firm’s stock is currently selling for $88 per share. Its last dividend (D₀) was $4.5, and dividends are expected to grow at a constant rate of 7.5%. The current risk free return offered by Treasury security is 2.5%, and the market portfolio’s return is 8%. Grand Island Hotel has a beta of 2.1. For the bond-yield-plus-risk-premium approach, the firm uses a risk premium of 3.9%.

(5) The firm adjusts its project WACC for risk by adding 1.8% to the overall WACC for high-risk projects and subtracting 2% for low-risk projects.

William knows that Grand Island Hotel executives have favored IRR in the past for making their capital budgeting decisions. His professor at Seattle U. said NPV was better than IRR. His textbook says that MIRR is also better than IRR. He is the new kid on the block and must be prepared to defend his recommendations.

First, however, William must finish the analysis and write his report. To help begin, he has formulated the following questions:

1. What is the firm’s cost of debt?

2. What is the cost of preferred stock for Grand Island Hotel?

3. Cost of common equity

(1) What is the estimated cost of common equity using the CAPM approach?

(2) What is the estimated cost of common equity using the DCF approach?

(3) What is the estimated cost of common equity using the bond-yield-plus-risk-premium approach?

(4) What is the final estimate for r_s?

4. What is Grand Island Hotel’s overall WACC?

5. Do you think the firm should use the single overall WACC as the hurdle rate for each of its projects? Explain.

6. What is the WACC for each project? Place your numerical solutions in Table 2.

7. Calculate all relevant capital budgeting measures for each project, and place your numerical solutions in Table 2.

Table 2

	A	B	C	D
WACC
NPV
IRR
MIRR

Answer 1

a]	Before tax cost of debt = YTM
	YTM using an online calculator = 9.51%
	[Inputs: Current price = $960; coupon 9%; Years to
	maturity 15, payment interval = 2]
	After tax cost of debt = 9.51%*(1-38%) =	5.90%
b]	Cost of preferred stock = 8.5/98 =	8.67%
c]	Constant dividend growth model:
	Cost of equity = 4.5*1.075/88+0.075 =	13.00%
	CAPM:
	Cost of equity = 2.5%+2.1*(8%-2.5%) =	14.05%
	Bond yield plus risk premium:
	Cost of equity = 9.51%+3.9% =	13.41%
	Final estimate for rs = (13%+14.05%+13.41%)/3 =	13.49%
d]	Overall WACC = 5.90%*45%+8.67%*5%+13.49%*50% =	9.83%
e]	No, the overall WACC should not be used as the
	discount rate for all the projects as the projects
	have different risks. Adjustments in the WACC for
	projects with lower/higher risk than the average
	projects.
f]	WACC of each project is:
	A = 9.83%+1.8% =	11.63%
	B = 9.83%+0 =	9.83%
	C = 9.83%-2.00% =	7.83%
	D = 9.83%+0% =	9.83%
g]	PROJECT A:
	Year	Cash flows	PVIF at 11.63%	PV at 11.63%	PVIF at 13%	PV at 13%	PVIF at 14%	PV at 14%	FVIF at 11.63%	FV at 11.63%
	0	$ -1,90,00,000	1.00000	$-1,90,00,000	1	$ -1,90,00,000	1	$ -1,90,00,000
	1	$       52,00,000	0.89582	$      46,58,246	0.88496	$      46,01,770	0.87719	$      45,61,404	1.39105	$    72,33,461
	2	$       83,00,000	0.80249	$      66,60,644	0.78315	$      65,00,117	0.76947	$      63,86,580	1.24613	$1,03,42,843
	3	$       61,00,000	0.71888	$      43,85,176	0.69305	$      42,27,606	0.67497	$      41,17,326	1.11630	$    68,09,430
	4	$       61,00,000	0.64399	$      39,28,313	0.61332	$      37,41,244	0.59208	$      36,11,690	1.00000	$    61,00,000
				$        6,32,380		$            70,738		$       -3,23,000		$3,04,85,734
	NPV =	$         6,32,380
	IRR = 13%+1%*70738/(70738+323000) =	13.18%
	MIRR = (30485734/19000000)^(1/4)-1 =	12.55%
	PROJECT B:
	Year	Cash flows	PVIF at 9.83%	PV at 9.83%	PVIF at 8%	PV at 8%	PVIF at 9%	PV at 9%	FVIF at 9.83%	FV at 9.83%
	0	$ -2,00,00,000	1.00000	$-2,00,00,000	1	$ -2,00,00,000	1	$ -2,00,00,000
	1	$       57,00,000	0.91050	$      51,89,839	0.92593	$      52,77,778	0.91743	$      52,29,358	1.32484	$    75,51,580
	2	$       80,00,000	0.82901	$      66,32,053	0.85734	$      68,58,711	0.84168	$      67,33,440	1.20626	$    96,50,103
	3	$       63,00,000	0.75481	$      47,55,296	0.79383	$      50,01,143	0.77218	$      48,64,756	1.09830	$    69,19,290
	4	$       44,00,000	0.68725	$      30,23,909	0.73503	$      32,34,131	0.70843	$      31,17,071	1.00000	$    44,00,000
				$      -3,98,902		$         3,71,763		$           -55,375		$2,85,20,973
	NPV =	$       -3,98,902
	IRR = 8%+1%*371763/(371763+55375) =	8.87%
	MIRR = (28520973/20000000)^(1/4)-1 =	9.28%
	PROJECT C:
	Year	Cash flows	PVIF at 7.83%	PV at 7.83%	PVIF at 10%	PV at 10%	PVIF at 11%	PV at 11%	FVIF at 7.83%	FV at 7.83%
	0	$ -1,89,00,000	1.00000	$-1,89,00,000	1	$ -1,89,00,000	1	$ -1,89,00,000
	1	$       60,80,000	0.92739	$      56,38,505	0.90909	$      55,27,273	0.90090	$      54,77,477	1.25377	$    76,22,938
	2	$       60,80,000	0.86004	$      52,29,069	0.82645	$      50,24,793	0.81162	$      49,34,664	1.16273	$    70,69,404
	3	$       60,80,000	0.79759	$      48,49,364	0.75131	$      45,67,994	0.73119	$      44,45,644	1.07830	$    65,56,064
	4	$       60,80,000	0.73968	$      44,97,231	0.68301	$      41,52,722	0.65873	$      40,05,084	1.00000	$    60,80,000
				$      13,14,168		$         3,72,782		$           -37,130		$2,73,28,406
	NPV =	$       13,14,168
	IRR = 10%+1%*372782/(372782+37130) =	10.91%
	MIRR = (27328406/18900000)^(1/4)-1 =	9.66%
	PROJECT D:
	Year	Cash flows	PVIF at 9.83%	PV at 9.83%	PVIF at 15%	PV at 15%	PVIF at 14%	PV at 14%	FVIF at 9.83%	FV at 9.83%
	0	$ -1,95,00,000	1.00000	$-1,95,00,000	1	$ -1,95,00,000	1	$ -1,95,00,000
	1	$       66,00,000	0.91050	$      60,09,287	0.86957	$      57,39,130	0.87719	$      57,89,474	1.32484	$    87,43,934
	2	$       81,00,000	0.82901	$      67,14,954	0.75614	$      61,24,764	0.76947	$      62,32,687	1.20626	$    97,70,729
	3	$       61,00,000	0.75481	$      46,04,335	0.65752	$      40,10,849	0.67497	$      41,17,326	1.09830	$    66,99,630
	4	$       61,00,000	0.68725	$      41,92,238	0.57175	$      34,87,695	0.59208	$      36,11,690	1.00000	$    61,00,000
				$      20,20,814		$       -1,37,562		$         2,51,177		$3,13,14,294
	NPV =	$       20,20,814
	IRR = 14%+1%*251177/(251177+137562) =	14.65%
	MIRR = (31314294/19500000)^(1/4)-1 =	12.57%
	CHOICE:
	The results are tabulated below:
	Project	NPV	IRR	MIRR	Discount Rate	Accept/Reject
	A	$         6,32,380	13.18%	12.55%	11.63%	Accept
	B	$       -3,98,902	8.87%	9.28%	9.83%	Reject
	C	$       13,14,168	10.91%	9.66%	7.83%	Accept
	D	$       20,20,814	14.65%	12.57%	9.83%	Accept
	Of the 4 mutually exclusive projects, Project B is to be rejected as it has negative NPV and IRR/MIRR are less than required
	rate of return.
	Of the remaining 3 projects, Project D with higher NPV, IRR and MIRR is to be selected.