Market value of equity =
400
2. Did not set up for new cost of capital: -1 point

Sheet1
Page 14
Value of the firm =
500
3. Used new firm value in computation: -1/2 point
The next step is to compute the value gained by stockholders in the buyback
4. Math errors: -1/2 point each
Number of shares bought back =
5
Premium paid on buyback =
5
Value gained by buyback investors
25
Remaining shares =
11
Premium on remaining shares =
2
Value gained by remaining shares
22
Total value gained =
47
The third step is to set the value gain, relative to the original firm value
(.09 - New Cost of capital)* 500/ New cost of capital = 47
New cost of capital =
8.23%
You could also solve the problem this way
Number of shares outstanding after the buyback
11
Price per share after buyback =
27
Value of equity =
297
Debt outstanding after buyback =
250
Value of firm after buyback =
547
Change in value =
47
Then, use the same third step as before to get the same answer
Problem 3
a. Duration of assets =
6.8
1. All or nothing, unless egregious math error
b. Duration of debt =
6.4
1. All or nothing, unless egregious math error
c. After acquisition of new business
1. Did not compute new asset duration: -1 point
Duration of assets =
7.25
2. Did not set up for new debt duration: -1 point
To set the duration of the debt to 7.25 years after the debt issue
3. Math errors: -1/2 point each
Let the value of new bonds issued be X
(Here is a test of the second part. If you plug in 7.25
Debt oustanding after =
5+X
and don't get the right answer, the second part of
(3/(5+X)) *4+ (2+X)/ (5+X) *10 = 7.25
the problem is set up incorrectly)
Solving for X
X =
$1.55
Check the answer
7.25
Spring 2014
Problem 1
Grading template
a. Current cost of capital
Current levered beta =
1.15
1. Wrong debt ratio: -1/2 point
Cost of equity =
8.7500% ! 3% + Beta *5%
2. Math errors: -1/2 point each
After-tax cost of debt =
3.00% ! Pre-tax cost of debt (1-.40)
Debt to capital ratio =
20%
Cost of capital =
7.600%
b. New cost of capital

Sheet1
Page 15
New debt to capital ratio =
60%
1. Wrong debt ratio: -1/2 point
New debt to equity ratio =
1.5
2. Did not adjust tax rate: -1 point
Unlevered beta =
1.00
3. Did not relever beta: -1 point
4. Other math errors: -1/2 point each
Interest expense on debt =
48
Operating income =
36
Maximum tax benefit on debt =
14.4
Tax benefit on debt =
30.00% !Max Tax Benefit/ Interest expense
Levered beta =
2.05
New cost of equity =
13.2500%
New cost of debt =
5.60%
New cost of capital =
8.6600%
Problem 2
Value of firm before buyback =
2400
Cost of capital before buyback =
10%
Growth rate in perpetuity =
2%
Approach 1: Value generated from buyback
Number of shares bought back =
40
1. Change in firm value incorrect: -1 point
Premium per share =
$5
2. Firm value incorrect: -1 point
Premium paid on buyback =
$200
3. Did not factor in growth: -1/2 point
4. Used wrong cost of capital in discounting: -1/2 point
Remaining shares =
60
Premium per share =
10
Premium to remaining shareholders
600
Total value added by buyback =
$800
Value added by buyback = 800 = 2400 *(.10-X)/(X -.02)
Solving for X
Cost of capital after buyback =
8.00%
Approach 2: Firm valuation
Value before = 2400 = Cash flow next year / (.10-.02)
Expected cash flow next year =
192
Value of equity after buyback =
1680
Value of debt after buyback =
1520
Total value after buyback =
3200

Sheet1
Page 16
Value after buyback = 3200 = 192/(X -.02)
Solve for X
Cost of capital after =
8.00%
Problem 3
a. Duration of assets today
Duration
Weight
Value
Hotel business
20
60%
600 ! Value of business = Debt + Equity = 800 + 200 = 1000
Travel business
2
40%
400
1. Weights incorrect: -1/2 point
Company assets
12.8
2. Math errors: -1/2 point
b. Duration of debt today

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- Cost Of Capital, Debt