Question

For this exercise, we assume that there are no taxes and financial markets are perfect. The ideal bank's interest rate (EAR) is 8% per year for all maturities. Company X owns one apartment building and has no other assets. Company X is 100% equity-financed;_ its revenue comes entirely from rental revenue of apartments it owns. We also assume that there are no cash costs, no depreciations, no investments, no working capital, therefore we have: rental revenue=EBIT=net income=free cash flow. Company X's rental revenue each year is random variable, whose distribution is as follows: 45 mio with 10% probability, 10 mio with 40% probability, 3 mio with 50% probability. The expected rental revenue is 10 mio. The distribution of rental revenue is assumed to be the same for every year in the future. In other words, Company expects to make 10 mio free cash flow per year forever.

a. Assume that the cost of capital for the unlevered equity is 13.333%, calculate .the value of the unlevered equity;
b. At the end of year 0, Company X borrows 15 mio dollars of perpetual debt with 8% interest rate, and pays 15 mio dollars as special diVidends. After the dividends and with 15 mio of debt, what is the value of the levered equity at the end of year 0? What is the cost of capital of the levered equity? Write down the expected· cash flow of the levered equity in Y1, Y2, Y3 andY 4.
c. Now, at the end of year 0, Company X has made the following announcement: it will borrow an additional amount of · 12.5 of perpetual debt at the end of the year 2 and will use the proceeds of the debt to pay a special dividend of the same amount to equity holders at the end of year 2. So after Y2, the total debt will be 2 7.5 mio. Assume that the debt cost is still 8%. Write down the expected cash flow of the levered equity in Y1, Y2, Y3, Y4. What is the cost of capital of the levered equity in Y1, Y2? What is the cost of capital of the levered equity after Y2? Can you find the value of the levered equity at end of YO by directly discounting all the future expected cash flows to the levered equity by appropriated discount rates?

Answer 1

a. Company X rental income every year - cash flow every year = $10 million; here growth rate = 0%

Since it is 100% equity financed, Cost of capital = 13.333%

Present value of future forever cash flow = 10 *(1+0%) / (13.333% - 0%)

Value of the firm X = $75 million

b.

Value of firm equity (i.e. value of firm) = $75 million

New 8% perpetual debt = $15 million

Cost of capital = (13.333% * 75 + 8% * 15) / (75+15) = 12.44%

Year	0	1	2	3	4
Rental	0	10	10	10	10
Special dividend	-15	0	0	0	0
New 8% perpetual debt	15	0	0	0	0
Interest on perpetual debt	0	-1.2	-1.2	-1.2	-1.2
Total cash flow	0	8.8	8.8	8.8	8.8

Excel formula:

C. Total debt after $12.5 million additional debt in year 2 = 15+12.5 = 27.5

Cost of capital in Year 1 and Year 2 = 12.44% (new 12.5 million debt issued at the end of year 2)

Weighted average cost of capital after year 2 = (13.333% * 75 + 8% * 27.5) / (75+27.5) = 11.90%

Year	0	1	2	3	Terminal value
Rental	0.0	10.0	10.0	10.0
Special dividend	-15.0	0.0	-12.5	0.0
New 8% perpetual debt	15.0	0.0	12.5	0.0
Interest on perpetual debt (8%)	0.0	-1.2	-1.2	-2.2
Total cash flow	0	8.8	8.8	7.8	65.5
Cost of capital	13.33%	12.44%	12.44%	11.90%
Discount factor	1.000	0.889	0.791	0.714	0.714
Discounted cash flow	0.0	7.8	7.0	5.6	46.8
Firm value					67.1

Terminal value at year 3 = Cash flow at year 3 * (1+growth rate) / (Cost of capital - growth rate)

= 7.8 * (1+0%) / (11.90% - 0)

= 65.6 million

Value of levered equity = Value of firm - total perpetual debt

= 67.1 - 27.5

Value of levered equity = $39.6 million