Charles has the following information about his firm, Gas Co. The equity beta is
ID: 2654523 • Letter: C
Question
Charles has the following information about his firm, Gas Co. The equity beta is 1.50 and the stock price is $10. He also knows the Tbill rate is 5% and the return on the S&P 500 is 15%. The firm is 40% debt financed. Assume the debt has a beta of 0.
a) Find the firm’s cost of capital.
b) Charles has decided to build 4 gas stations in Detroit. The initial construction will cost $1,000,000 and will generate expected cash flows of $120,000 forever. Charles believes the covariance between the returns on the project and the returns on the market is 20%. He also believes that the standard deviation of the market is 40%. The project is expected to return 15%.
- If Gas Co. uses the company cost of capital for accepting projects, will it build the stations? Why? (Assume the company's cost of capital is the number you determined in part a).
- Based on the CAPM, should Gas Co. build the shops? Why?
c) Sara is a real estate expert. She advises Charles to diversify his investments by building in Detroit, Atlanta, Boston, and San Diego. Charles claims this is unnecessary because he has diversified by investing in 4 different stations in Detroit. Why might Charles be better diversified by taking Sara's advice?
Explanation / Answer
WACC= Wd[Kd(1-t)]+We(Ke)
Where:
Wd =Weight of debt =40%=0.4
Kd=Cost of debt financing =T-bill rate =0.05
T=tax rate=30% (assumed)=0.3
We=Weight of equity = 60%=0.6 which is(1-Debt)
Ke = cost of equity calculated by CAPM Model as below:
Er = RFR+Beta(Rm-RFR)
Where
RFR = risk free return =0.05
Rm= Market return =0.15
Beta=1.5
Therefore, Er = 0.05 + 1.5(0.15-0.05)
Er=0.2=20%
Therefore ke in WACC formula will be 0.2
Ke= cost of equity=0.2
WACC = 0.4*0.05*(1-0.3) + 0.6*0.2
WACC=0.134 or 13.4%
WACC=13.4%
NPV = Cash inflow in yr1/COC + Cash inflow in yr2/COC^2 + Cash inflow in yr3/COC^3……….. – Initial Investment
The below table shows the NPV calculation
Cash Inflow
Cost of Capital
Year
Present Value
120000
1.134
1
105820.1058
120000
1.134
2
93315.78996
120000
1.134
3
82289.05641
120000
1.134
4
72565.30547
120000
1.134
5
63990.5692
120000
1.134
6
56429.07337
120000
1.134
7
49761.08763
120000
1.134
8
43881.02965
120000
1.134
9
38695.79335
120000
1.134
10
34123.27455
120000
1.134
11
30091.07104
120000
1.134
12
26535.33601
120000
1.134
13
23399.7672
120000
1.134
14
20634.71535
120000
1.134
15
18196.39801
120000
1.134
16
16046.20636
120000
1.134
17
14150.09379
120000
1.134
18
12478.03685
120000
1.134
19
11003.55984
120000
1.134
20
9703.315553
120000
1.134
21
8556.715655
120000
1.134
22
7545.604634
120000
1.134
23
6653.97234
120000
1.134
24
5867.700477
120000
1.134
25
5174.339045
120000
1.134
26
4562.90921
120000
1.134
27
4023.729462
120000
1.134
28
3548.262313
120000
1.134
29
3128.979112
120000
1.134
30
2759.240839
120000
1.134
31
2433.19298
120000
1.134
32
2145.672822
120000
1.134
33
1892.127709
120000
1.134
34
1668.542953
120000
1.134
35
1471.378265
120000
1.134
36
1297.511698
120000
1.134
37
1144.19021
120000
1.134
38
1008.986076
120000
1.134
39
889.7584442
120000
1.134
40
784.6194393
Initial Outlay
1000000
NPV of project after 40 years
-110333
The NPV after 40 years also shows a negative value. Therefore the company should not build the gas stations.
Based on CAPM:
Cov(Rj,Rm)=20%=0.2
Std. dev of Project =40%=0.4
Variance =0.42 =0.16
Therefore, beta of the project = 0.2/0.16=1.25
Since the beta value is more than 1, this is a high risk project, that would be undertaken by the company. If the company wants to reduce the risk and increase the cash flows for the gas stations, building shops would be necessary.
Considering that the present cash flows from the gas station would not be profitable as per the above table, the construction of shops in the gas station will improve the cash flows and make the project feasible.
Therefore, Charles should consider diversifying into other cities as per Sara’s recommendation.
WACC= Wd[Kd(1-t)]+We(Ke)
Where:
Wd =Weight of debt =40%=0.4
Kd=Cost of debt financing =T-bill rate =0.05
T=tax rate=30% (assumed)=0.3
We=Weight of equity = 60%=0.6 which is(1-Debt)
Ke = cost of equity calculated by CAPM Model as below:
Er = RFR+Beta(Rm-RFR)
Where
RFR = risk free return =0.05
Rm= Market return =0.15
Beta=1.5
Therefore, Er = 0.05 + 1.5(0.15-0.05)
Er=0.2=20%
Therefore ke in WACC formula will be 0.2
Ke= cost of equity=0.2
WACC = 0.4*0.05*(1-0.3) + 0.6*0.2
WACC=0.134 or 13.4%
WACC=13.4%
NPV = Cash inflow in yr1/COC + Cash inflow in yr2/COC^2 + Cash inflow in yr3/COC^3……….. – Initial Investment
The below table shows the NPV calculation
Cash Inflow
Cost of Capital
Year
Present Value
120000
1.134
1
105820.1058
120000
1.134
2
93315.78996
120000
1.134
3
82289.05641
120000
1.134
4
72565.30547
120000
1.134
5
63990.5692
120000
1.134
6
56429.07337
120000
1.134
7
49761.08763
120000
1.134
8
43881.02965
120000
1.134
9
38695.79335
120000
1.134
10
34123.27455
120000
1.134
11
30091.07104
120000
1.134
12
26535.33601
120000
1.134
13
23399.7672
120000
1.134
14
20634.71535
120000
1.134
15
18196.39801
120000
1.134
16
16046.20636
120000
1.134
17
14150.09379
120000
1.134
18
12478.03685
120000
1.134
19
11003.55984
120000
1.134
20
9703.315553
120000
1.134
21
8556.715655
120000
1.134
22
7545.604634
120000
1.134
23
6653.97234
120000
1.134
24
5867.700477
120000
1.134
25
5174.339045
120000
1.134
26
4562.90921
120000
1.134
27
4023.729462
120000
1.134
28
3548.262313
120000
1.134
29
3128.979112
120000
1.134
30
2759.240839
120000
1.134
31
2433.19298
120000
1.134
32
2145.672822
120000
1.134
33
1892.127709
120000
1.134
34
1668.542953
120000
1.134
35
1471.378265
120000
1.134
36
1297.511698
120000
1.134
37
1144.19021
120000
1.134
38
1008.986076
120000
1.134
39
889.7584442
120000
1.134
40
784.6194393
Initial Outlay
1000000
NPV of project after 40 years
-110333
The NPV after 40 years also shows a negative value. Therefore the company should not build the gas stations.
Based on CAPM:
Cov(Rj,Rm)=20%=0.2
Std. dev of Project =40%=0.4
Variance =0.42 =0.16
Therefore, beta of the project = 0.2/0.16=1.25
Since the beta value is more than 1, this is a high risk project, that would be undertaken by the company. If the company wants to reduce the risk and increase the cash flows for the gas stations, building shops would be necessary.
Considering that the present cash flows from the gas station would not be profitable as per the above table, the construction of shops in the gas station will improve the cash flows and make the project feasible.
Therefore, Charles should consider diversifying into other cities as per Sara’s recommendation.
Cash Inflow
Cost of Capital
Year
Present Value
120000
1.134
1
105820.1058
120000
1.134
2
93315.78996
120000
1.134
3
82289.05641
120000
1.134
4
72565.30547
120000
1.134
5
63990.5692
120000
1.134
6
56429.07337
120000
1.134
7
49761.08763
120000
1.134
8
43881.02965
120000
1.134
9
38695.79335
120000
1.134
10
34123.27455
120000
1.134
11
30091.07104
120000
1.134
12
26535.33601
120000
1.134
13
23399.7672
120000
1.134
14
20634.71535
120000
1.134
15
18196.39801
120000
1.134
16
16046.20636
120000
1.134
17
14150.09379
120000
1.134
18
12478.03685
120000
1.134
19
11003.55984
120000
1.134
20
9703.315553
120000
1.134
21
8556.715655
120000
1.134
22
7545.604634
120000
1.134
23
6653.97234
120000
1.134
24
5867.700477
120000
1.134
25
5174.339045
120000
1.134
26
4562.90921
120000
1.134
27
4023.729462
120000
1.134
28
3548.262313
120000
1.134
29
3128.979112
120000
1.134
30
2759.240839
120000
1.134
31
2433.19298
120000
1.134
32
2145.672822
120000
1.134
33
1892.127709
120000
1.134
34
1668.542953
120000
1.134
35
1471.378265
120000
1.134
36
1297.511698
120000
1.134
37
1144.19021
120000
1.134
38
1008.986076
120000
1.134
39
889.7584442
120000
1.134
40
784.6194393
Initial Outlay
1000000
NPV of project after 40 years
-110333