Question

Mrs. Fields runs a chain of BBQ joints called Fields BBQ House (FBH). Currently FBH uses only equity capital. Mrs. Fields was approached by representatives from Lenders Inc. who have pointed out to her that FBH’s cost of unlevered equity capital is 15% and the cost of debt capital is only 6%. The reps said her company (which produces before-tax operating cash flows of $5 million per year) would benefit from using some debt. They recommend that FBH issues $12 million worth of bonds and use the entire proceeds to repurchase $12 million worth of its own stocks. Assume that both the firm’s cash flows and the debt are perpetual, and FBH’s marginal corporate tax rate is 30%.

a) What is the current value of the firm without debt?

b) If Mrs. Fields follows Lenders Inc.’s plan what would be the value of the firm? What would be the cost of equity of the firm?

c) Now assume interest expenses were not tax deductible. If Mrs. Fields still followed Lenders’ advice to issue debt and repurchase an equal amount of equity, even though interest expenses were not tax deductible. What would be the value of the firm? What would be the cost of equity of the firm?

Answer 1

(a) VALUE OF UNLEVERED FIRM = EBIT (1-t)/ Ke = 5 (1-0.30) /0.15 = $ 23.33 MILLION

(b) NOW IF DEBT IS ISSUED

VALUE OF LEVERED FIRM = VALUE OF UNLEVERED FIRM + DEBT (TAX RATE)

VALUE OF LEVERED FIRM = $23.33 MILLION + ($12 MILLION *30%) = $ 26.93 MILLION

VALUE OF EQUITY = VALUE OF LEVERED FIRM - VALUE OF DEBT

VALUE OF EQUITY = $26.93 - $12 = $ 14.93 MILLION

NET INCOME AFTER TAXES = (EBIT - I)(1-t) = (5 - 0.72) (1-0.3) = $ 2.996 MILLION

THE COST OF EQUITY = $2.996 MILLION/ $14.93 MILLION = 0.2007 = 20.07%

(c ) IF INTEREST IS NOT TAX DEDUCTIBLE

VALUE OF LEVERED FIRM = (NET INCOME AFTER TAX - INTEREST)/Ke + (INTEREST/ Kd)

VALUE OF LEVERED FIRM = (3.5 - 0.72)(1-0.30)/0.15 + (0.72/ 0.06) = 18.533 + 12 = $ 30.533 MILLION

COST OF EQUITY WILL BE = 15% ( NO CHANGE)

ANY DOUBTS, FEEL FREE TO ASK