Cost of Capital Final

Homework on Estimation of Cost of Capital: 20 Points
A diversified firm plans to sell a division mainly engaged in operating a regional airline. You
have been assigned the task of estimating an acceptable value for the division before the firm
engages an Investment banker to negotiate with potential buyers. However, the CEO and the CFO
disagree about discount rate that should be used in estimating value using discounted cash flow
method. The CEO believes that it should be firm’s WACC--- 6.4 percent derived as follows:
 Debt-equity ratio (D/E) =0.5
 Cost of debt (kD) = 6 percent
 Risk Free rate (RF) =5 percent
 Market Risk Premium (MRP) = 5 percent
 Tax Rate (T) = 30 percent
 Levered Equity Beta (βE) = 0.5
 Cost of Equity (kE) = RF + MRP x βE = 5% + 5% x 0.5 = 7.5%
 WACC = kD(1-T)x D/(D+E) + kE x E/D+E = 6% (1-0.3) x1/3 +7.5% x2/3 = 6.4%
The CFO believes that firm’s WACC is inappropriate discount rate for the airline division as its
risk is higher due to greater debt compared to other divisions. To assist you with the task of
deriving a discount rate for the airline division, he has provided data on comparable firms.
Part A: Assume that kD and D/E for division are equal to average of comparable airlines.
Further assume that other parameters --- RF, MRP and T—remain the same. Estimate an
appropriate discount rate for the division using following table. (15 Points)
A
B
C
D
E
Average
1. βE
1.20
0.95
1.35
1.45
1.55
1.3
2. D/E
1.25
1.85
1.35
1.70
3.40
1.91
3. kD %
6
7
7.5
7.25
8.50
7.25
1
1
4. βA (Business Risk) βA = βE /{1+D/E}
0.53
0.33
0.57
0.54
0.35
0.466
5. % Business Risk 4/1
53%
33%
57%
54%
35%
47%
6. % Financial Risk (100-line 5)
47%
67%
43%
46%
65%
53%
7. βE for the Division ; βA x{1+ (1-t) D/E}
1.09
8. kE (Division) = RF + MRP x βE( for the division)
5.054
9.WACC:(Div) ( = kD(1-T)x D/(D+E) + kE x E/D+E) 5.075
1. You can also use alternate formula for βA = βE/{1+(1-t) D/E} and βE = βA x{1+ (1-t) D/E}
Part B: If you used firm’s WACC instead of divisional WACC, what effect would that have
on the valuation? Limit your answer to 50 words. No Calculations are necessary. (5 Points)

As the projects risk profile is different from that of the firm’s hence the firm is not the
right proxy for the project as the investors would require project’s cost of capital not of
firm’s.so it is a superior decision-making compared to ignoring differential risk and using
WACC for everything. Ignoring differential risk would result in accepting or rejecting
projects based on an invalid premise.

Homework on Discount Rate

1

Suren Mansinghka

Homework on Discount Rate

2

Suren Mansinghka