Assignment 1
You have been asked to value a firm with expected annual after-tax cash flows, before debt payments, of $100 million a year in perpetuity. The firm has a cost of equity of 10%, a market value of equity of $750 million and a market value of debt of $500 million (this is also the book value). The debt is perpetual and the after-tax interest rate on debt is 5%. The company has no non-operating activities.
a. Estimate the value of the firm and the value of the equity based upon this value.
b. Estimate the value of equity, by discounting the cash flows to equity at the cost of equity.
c. Now assume that you had been told that the market value of equity was $850 million and that all of the other information remained unchanged. Answer parts a and b, using these new values.
d. In practice, what needs to happen for the two valuation approaches (FCFF and FCFE) to give the same estimate of value?
Assignment 2
a. Using the financial statements and other information that you have for MPR, and assuming a 5% perpetual growth rate in the FCFE, value the equity using the FCFE method.
b. Does this value equal the estimated value using the FCFF method? Why or why not?
Assignment 3
IO Taxes Inc. is a large but privately-held all-equity firm in the tax planning industry. The firm has been enjoying a nice 20% annual growth in its FCFE due to the highly anticipated increase in taxes related to the massive baby-boomers retirement wave. IO’s FCFE is expected to be $5 million next year. The growth rate is expected to be the same for an additional year after that and then management expects the FCFE’s growth rate to cool down to 4% in perpetuity.
IO Taxes has 10 million shares outstanding and it has $10 million in non-operating cash (invested mostly in Treasury bills).
While IO Taxes is not publicly traded, its close competitor, H&R Rock Inc., is and has an unlevered and unadjusted equity beta of 1.3.
a. Based on the available information, please estimate IO’s cost of equity.
b. Estimate the intrinsic value of each share of stock.
Assignment 1:
Question a:
|
Calculation of value of firm |
|
|
Cost of equity = |
10.00% |
|
Market value of equity = |
750 |
|
Market value of debt = |
500 |
|
After-tax interest rate on debt = |
5.00% |
|
Debt/Capital ratio = |
0.4 |
|
Cost of capital = |
8.00% |
|
Cash flow to firm = |
$100.00 |
|
Value of firm= |
$1,250.00 |
Question b:
|
Calculation of value of equity |
|
|
Cash flow to firm |
$100.00 |
|
- Interest (1-t) |
$25.00 |
|
= Cash flow to equity |
$75.00 |
|
Value of equity |
$750.00 |
Question c:
|
Cost of equity = |
10.00% |
|
Market value of equity = |
850 |
|
Market value of debt = |
500 |
|
After-tax interest rate on debt = |
5.00% |
|
Debt/Capital ratio = |
0.37 |
|
Cost of capital = |
8.15% |
|
Cash flow to firm = |
$100.00 |
|
Value of firm= |
$1,227.27 |
|
Calculation of value of equity |
|
|
Cash flow to firm |
$100.00 |
|
- Interest (1-t) |
$25.00 |
|
= Cash flow to equity |
$75.00 |
|
Value of equity |
$750.00 |
Question d:
In case of FCFF an FCFE valuation method, it is important for the business to not to have depreciation and amortization expenses, capital expenditure and interest expenses in order to compute and get the same amount of average cash flows of the business. These items create differentiation in the cash flow of the business and affect the valuation process of the business (Gibson, 2011).
Assignment 2:
Question a:
|
FCFE valuation model |
||||
|
2015 |
2016 |
2017 |
||
|
Net income |
26592.7 |
27445.8 |
31945.7 |
|
|
Add: Depreciation & amortization |
0 |
0 |
||
|
Add: Changes in WC |
911.8 |
5249.7 |
||
|
Add: CAPEX |
11042 |
10458 |
||
|
Add: Net borrowings |
6808 |
7162 |
||
|
46207.6 |
54815.4 |
Average =50511.5 |
||
|
Present value of discrete cash flows for next 10 years |
||||
|
Year |
FCFF ($'000) |
PVF @10% |
PV of Cash Flows |
|
|
1 |
53,037.08 |
0.909 |
48,215.52 |
|
|
2 |
55,688.93 |
0.826 |
46,023.91 |
|
|
3 |
58,473.38 |
0.751 |
43,931.91 |
|
|
4 |
61,397.04 |
0.683 |
41,935.01 |
|
|
5 |
64,466.90 |
0.621 |
40,028.87 |
|
|
6 |
67,690.24 |
0.564 |
38,209.38 |
|
|
7 |
71,074.75 |
0.513 |
36,472.59 |
|
|
8 |
74,628.49 |
0.467 |
34,814.74 |
|
|
9 |
78,359.92 |
0.424 |
33,232.25 |
|
|
10 |
82,277.91 |
0.386 |
31,721.70 |
|
|
Total |
394,585.87 |
|||
Assumptions: It has been estimated that the cost of capital of the business is 6%.
|
FCFE valuation model |
||||
|
2015 |
2016 |
2017 |
||
|
EBIT |
44321.1 |
45743 |
53242.9 |
|
|
Tax rate |
17728.4 |
18297.2 |
21297.2 |
|
|
EAT |
26592.7 |
27445.8 |
31945.7 |
|
|
ADD: Noncash charges |
0 |
0 |
||
|
Add: Changes in WWC |
911.8 |
5249.7 |
||
|
Less: Capital expenditure |
11042 |
10458 |
||
|
81355.8 |
101277.5 |
91316.65 |
||
|
Present value of discrete cash flows for next 10 years |
||||
|
Year |
FCFF ($'000) |
PVF @10% |
PV of Cash Flows |
|
|
1 |
95,882.48 |
0.909 |
87,165.89 |
|
|
2 |
100,676.61 |
0.826 |
83,203.81 |
|
|
3 |
105,710.44 |
0.751 |
79,421.82 |
|
|
4 |
110,995.96 |
0.683 |
75,811.73 |
|
|
5 |
116,545.76 |
0.621 |
72,365.75 |
|
|
6 |
122,373.04 |
0.564 |
69,076.39 |
|
|
7 |
128,491.70 |
0.513 |
65,936.56 |
|
|
8 |
134,916.28 |
0.467 |
62,939.44 |
|
|
9 |
141,662.10 |
0.424 |
60,078.56 |
|
|
10 |
148,745.20 |
0.386 |
57,347.71 |
|
|
Total |
713,347.66 |
|||
Question b:
The computation in question a explains that the value of equity in both the methods, FCFF and FCFE is different because of the changes in the depreciation and amortization expenses, capital expenditure and interest expenses of the business. These factors have affected the total value of equity of the business (Higgins, 2012).
Assignment 3:
Question a:
|
Cost of Equity: CAPM model |
|
|
A. Risk free rate |
3.20% |
|
B. Market rate of return |
5.40% |
|
C. Beta |
1.3 |
|
D. CAPM |
6.06% |
Question b:
|
Valuation of equity taking free cash flows of firm |
|||
|
Past average |
|||
|
FCFF ($'000) |
5.00 |
||
|
Growth rate |
20.00% |
Applied for next 10 years |
|
|
Perpetual growth rate |
4.00% |
Applied after 10 years |
|
|
Estimated Free cash flows for firm |
|||
|
Year |
FCFF ($' M) |
Remarks |
|
|
2018 |
6.00 |
=5*(1+20%) |
|
|
2019 |
7.20 |
||
|
2020 |
7.49 |
||
|
2021 |
7.79 |
||
|
2022 |
8.10 |
||
|
2023 |
8.42 |
||
|
2024 |
8.76 |
||
|
2025 |
9.11 |
||
|
2026 |
9.47 |
||
|
2027 |
9.85 |
||
|
Terminal cash flows |
10.25 |
=9.85*(1+4%) |
|
|
Present value of discrete cash flows for next 10 years |
|||
|
Year |
FCFF ($'000) |
PVF @6.06% |
PV of Cash Flows |
|
1 |
6.00 |
0.943 |
5.66 |
|
2 |
7.20 |
0.889 |
6.40 |
|
3 |
7.49 |
0.838 |
6.28 |
|
4 |
7.79 |
0.790 |
6.15 |
|
5 |
8.10 |
0.745 |
6.03 |
|
6 |
8.42 |
0.703 |
5.92 |
|
7 |
8.76 |
0.662 |
5.80 |
|
8 |
9.11 |
0.625 |
5.69 |
|
9 |
9.47 |
0.589 |
5.58 |
|
10 |
9.85 |
0.555 |
5.47 |
|
Total |
58.99 |
||
|
Present value of terminal cash flows |
|||
|
Terminal cash flows |
10.25 |
73.51 |
|
|
Total firm value |
132.50 |
||
|
Less: Value of Debt |
10.00 |
||
|
Total value of Equity |
122.50 |
||
|
No of Shares Outstanding |
10.00 |
||
|
Per share value of value of equity (intrinsic value) |
12.25 |
||
References:
Gibson, C. H. (2011). Financial reporting and analysis. South-Western Cengage Learning.
Higgins, R. C. (2012). Analysis for financial management. McGraw-Hill/Irwin.
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