Question

2. Past Perfect Inc. is a small firm that sells antique furnishings. In the most recent year, the firm generated $ 4 million in after-tax operating income on revenues of $ 40 million; the firm reported book value of equity of $ 8 million and book value of debt of $ 4 million at the beginning of the year. During the year, the firm invested $2 million in a new warehouse for furniture (its only cap ex) and reported depreciation of $1 million in its income statement. The firm’s only working capital item is its inventory, which increased by $ 200,000 during the course of the year. The cost of capital for the firm is expected to be 12% for the next 3 years and 10% thereafter. You have been asked to appraise the value of the company. Assuming that the firm maintains its existing return on capital and reinvestment rate for the next 3 years, estimate the expected free cash flow to the firm each year for the next 3 years. b. Estimate the value of the firm at the end of year 3, assuming that the return on capital stays at the current level but the growth rate drops to 3%. c. Assuming that Past Perfect Inc. has 5 million shares outstanding, estimate the value of equity per share. (You can assume that the book value of debt = market value of debt, and that the debt remained unchanged over the most recent year). You can also assume no cash holdings.

Answer 1

a). Calculation of expected growth rate:

FCFF for the next three years:

b). Terminal value at the end of 3 years:

ROC = 33.33%; g = 3%, so reinvestment rate = g/ROC = 3%/33.33% = 9%

After-tax operating income in Year 4 = After-tax op. income in Year 3*(1+g) = 5,324,000*(1+3%) = 5,483,720

Reinvestment in Year 4 = After-tax op.income*reinvestment rate =  5,483,720*9% = 493,534.80

FCFF in Year 4 = after-tax op.income - reinvestment

= 5,483,720 - 493,534.80 = 4,990,185.20

Terminal value at the end of 3 years = FCFF in Year 4/(stable cost of capital -g)

= 4,990,185.20/(10%-3%) = 71,288,360 (value of the firm at the end of Year 3)

c). Present firm value = sum of present values (PV) of all future cash flows

= 2,750,000 + 2,700,892.86 + 2,652,662.63 + 71,288,360/(1+12%)^3 = 58,845,202.03

Total equity value = firm value - debt value = 69,203,614.49 - 4,000,000 = 54,845,202.03

Per share value = total equity value/number of shares = 54,845,202.03/5,000,000 = 10.97 per share