For this exercise, we assume that there are no taxes and financial markets are perfect. The...

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Finance

For this exercise, we assume that there are no taxes andfinancial markets are perfect. The ideal bank's interest rate (EAR)is 8% per year for all maturities. Company X owns one apartmentbuilding and has no other assets. Company X is 100%equity-financed;_ its revenue comes entirely from rental revenue ofapartments it owns. We also assume that there are no cash costs, nodepreciations, no investments, no working capital, therefore wehave: rental revenue=EBIT=net income=free cash flow. Company X'srental revenue each year is random variable, whose distribution isas follows: 45 mio with 10% probability, 10 mio with 40%probability, 3 mio with 50% probability. The expected rentalrevenue is 10 mio. The distribution of rental revenue is assumed tobe the same for every year in the future. In other words, Companyexpects to make 10 mio free cash flow per year forever.
a. Assume that the cost of capital for the unlevered equity is13.333%, calculate .the value of the unlevered equity;
b. At the end of year 0, Company X borrows 15 mio dollars ofperpetual debt with 8% interest rate, and pays 15 mio dollars asspecial diVidends. After the dividends and with 15 mio of debt,what is the value of the levered equity at the end of year 0? Whatis the cost of capital of the levered equity? Write down theexpected· cash flow of the levered equity in Y1, Y2, Y3 andY4.
c. Now, at the end of year 0, Company X has made the followingannouncement: it will borrow an additional amount of · 12.5 ofperpetual debt at the end of the year 2 and will use the proceedsof the debt to pay a special dividend of the same amount to equityholders at the end of year 2. So after Y2, the total debt will be 27.5 mio. Assume that the debt cost is still 8%. Write down theexpected cash flow of the levered equity in Y1, Y2, Y3, Y4. What isthe cost of capital of the levered equity in Y1, Y2? What is thecost of capital of the levered equity after Y2? Can you find thevalue of the levered equity at end of YO by directly discountingall the future expected cash flows to the levered equity byappropriated discount rates?

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a Company X rental income every year cash flow every year 10 million here growth rate 0Since it is 100 equity financed Cost of capital 13333Present value of future forever cash flow 10 10 13333 0Value of the firm X 75 millionbValue of See Answer

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Transcribed Image Text

For this exercise, we assume that there are no taxes andfinancial markets are perfect. The ideal bank's interest rate (EAR)is 8% per year for all maturities. Company X owns one apartmentbuilding and has no other assets. Company X is 100%equity-financed;_ its revenue comes entirely from rental revenue ofapartments it owns. We also assume that there are no cash costs, nodepreciations, no investments, no working capital, therefore wehave: rental revenue=EBIT=net income=free cash flow. Company X'srental revenue each year is random variable, whose distribution isas follows: 45 mio with 10% probability, 10 mio with 40%probability, 3 mio with 50% probability. The expected rentalrevenue is 10 mio. The distribution of rental revenue is assumed tobe the same for every year in the future. In other words, Companyexpects to make 10 mio free cash flow per year forever.a. Assume that the cost of capital for the unlevered equity is13.333%, calculate .the value of the unlevered equity;b. At the end of year 0, Company X borrows 15 mio dollars ofperpetual debt with 8% interest rate, and pays 15 mio dollars asspecial diVidends. After the dividends and with 15 mio of debt,what is the value of the levered equity at the end of year 0? Whatis the cost of capital of the levered equity? Write down theexpected· cash flow of the levered equity in Y1, Y2, Y3 andY4.c. Now, at the end of year 0, Company X has made the followingannouncement: it will borrow an additional amount of · 12.5 ofperpetual debt at the end of the year 2 and will use the proceedsof the debt to pay a special dividend of the same amount to equityholders at the end of year 2. So after Y2, the total debt will be 27.5 mio. Assume that the debt cost is still 8%. Write down theexpected cash flow of the levered equity in Y1, Y2, Y3, Y4. What isthe cost of capital of the levered equity in Y1, Y2? What is thecost of capital of the levered equity after Y2? Can you find thevalue of the levered equity at end of YO by directly discountingall the future expected cash flows to the levered equity byappropriated discount rates?