Question

. ABC is considering an acquisition of XYZ. XYZ has a capital structure of 60% debt and 40% equity, with a current book value of $15 million in assets. XYZ’s pre-merger beta is 1.36 and is not likely to be altered as a result of the proposed merger. ABC’s pre-merger beta is 1.02, and both it and XYZ face a 40% tax rate. ABC’s capital structure is 50% debt and 50% equity, and it has $34 million in total assets.

The net cash flows from XYZ available to ABC’s stockholders are estimated at $3.0 million for each of the next three years and a terminal value of $15.0 million in Year 4.

Additionally, new debt issued by the combined firm would yield 11% after-tax, and the cost of equity is estimated at 12.50%. Currently, the risk-free rate is 4.5% and the market return is 10.55%.                                                                                                                                     

A. What is the appropriate discount rate ABC should use to discount the equity cash flows from XYZ?

B. What is the present value (to the nearest thousand) of the XYZ cash inflows to ABC?

C. If the acquisition price of XYZ is 145% of XYZ’s current book value of assets, should ABC proceed with the acquisition?

Answer 1

A.  the appropriate discount rate ABC should use to discount the equity cash flows from XYZ is cost of equity of XYZ.

cost of equity of XYZ = risk-free rate + XYZ's beta*(market return - risk-free rate) = 4.5% + 1.36*(10.55% - 4.5%) = 4.5% + 1.36*6.05‬% = 4.5% + 8.228‬% = 12.728‬%

B. Present value of XYZ cash inflows = Year 1 net cash flow/(1+cost of equity) + Year 2 net cash flow/(1+cost of equity)2 + Year 3 net cash flow/(1+cost of equity)3 + terminal value/(1+cost of equity)3

Present value of XYZ cash inflows = $3/(1+0.12728) + $3/(1+0.12728)2 + $3/(1+0.12728)3 + $15/(1+0.12728)3

terminal value in year 4 is at the end of year 3. so it will be discounted for 3 years only.

Present value of XYZ cash inflows = $3/1.12728 + $3/1.127282 + $3/1.127283 + $15/1.127283

Present value of XYZ cash inflows = $3/1.12728 + $3/1.2707601984‬ + $3/1.432502556452352‬ + $15/1.432502556452352‬

Present value of XYZ cash inflows = $2.6612731530764317649563551202895‬ + $2.3607915984284576724117833371386‬ + $2.0942371003020169544494565122583‬ + $10.471185501510084772247282561292‬ = $17.587 million

the present value (to the nearest thousand) of the XYZ cash inflows to ABC is $17.587 million.

C. acquisition price of XYZ = $15 million*145% = $21.75‬ million

ABC should not proceed with the acquisition because the acquisition price of XYZ of $21.75 million is higher than the present value of the XYZ cash inflows to ABC of $17.587 million.