Question

Firm A is considering a merger with Firm B. The current market value of A is $20,000,000 and the volatility of asset return is 58% percent. A also has a zero coupon bond with a face value of $8,000,000 that matures in 3 years. B’s market value is $9,000,000 with standard deviation of asset return of 70% and a zero coupon bond of $3,000,000 that matures in 3 years. The continuously compounded risk free rate is 4%. After the merger the combined company will have asset volatility of 48%. What are the current market values of debt and equity for A, B, and the combined firm? You need to compute 6 values (1 for D and 1 for E for the three firms: A, B, and (A+B).

Answer 1

Current market value of debt for firm A = Face value of ZCB/[(1+risk free rate)^3] = $8,000,000/[(1+0.04)^3] = $8,000,000/(1.04^3) = $8,000,000/1.124864 = $7,111,970.87

Current market value of equity for firm A = Current market value of firm A - Current market value of debt for firm A = $20,000,000-$7,111,970.87 = $12,888,029.13

Current market value of debt for firm B = Face value of ZCB/[(1+risk free rate)^3] = $3,000,000/[(1+0.04)^3] = $3,000,000/(1.04^3) = $3,000,000/1.124864 = $2,666,989.08

Current market value of equity for firm B = Current market value of firm B - Current market value of debt for firm B = $9,000,000-$2,666,989.08 = $6,333,010.92

Current market value of debt for merged firm (A+B) = Face value of ZCB/[(1+risk free rate)^3] = ($8,000,000+$3,000,000)/[(1+0.04)^3] = $11,000,000/(1.04^3) = $11,000,000/1.124864 = $9,778,959.95

Current market value of equity for merged firm (A+B) = (Current market value of firm A+Current market value of firm B) - Current market value of debt for merged firm (A+B) = ($20,000,000+$9,000,000-$9,778,959.95 = $19,221,040.05

Note: ZCB=Zero coupon bond; Volatality is irrelevant; assume there is no synergy benefit.