Question

Your firm is considering expanding its operations which represent the same risk as your current operations. It’s expected to return additional cash flows of $10,000,000 at the end of each of the first five years and $7,000,000 at the end of each of the subsequent five years and a salvage value of $20,000,000 at the end of its 10-year use. Your firm is financed with $80,000,000 in $1,000 par bonds paying semi-annual coupons for an annual coupon rate of 6%, due in 20 years. They currently sell @105. Additionally, your firm is financed with $20,000,000 in common equity currently selling for $10/share which shareholders expect to continue to receive $0.25/share per quarter for the foreseeable future. You may annualize the coupons and dividends for this capital budgeting problem and assume negligible changes in the current expectations of inflation and risk. Your firm pays 40% in taxes. Remember to diagram the cf/time line where applicable.

1.)What is the most you would pay for this expansion? Would you pay more, less, or the same if immediately (a) share prices increase, (b) corporate income tax rates decrease, or (c) your bonds sell at par?

Answer 1

Lets first calculate the WACC,

cost of equity, Ke = (Dividend / Current price) + growth rate

= $1 / $10 + 0% = 10% (growth rate is 0% as there is no increase in dividend in forseeable future)

Kd = YTM of the bond

To calculate the YTM use bond valuation formula and calculate YTM using excel or hit and trial method.

Coupon rate = $60 (annualized)

current rice = 1050 (per 1000 par value)

T = 20

YTM or Kd = 5.58%

WACC = (5.58*(1-0.40) * 0.8) + 10 * 0.2

= 4.68% (this would be our discount rate)

Now to find what would be most we would pay our PV of all the future cashflows must be atleast equal to our initial investment so that our NPV is atlease equal to or greater than initial investment

initial investment = Cf1 / (1+r)^1 + Cf2 / (1+r)^2 +........+ Cf10 / (1+r)^10

Year Cash flows PV 1 $10,000,000 $9,552,923 2 $10,000,000 $9,125,834 3 $10,000,000 $8,717,839 4 $10,000,000 $8,328,085 5 $10,000,000 $7,955,756 6 $7,000,000 $5,320,051 7 $7,000,000 $5,082,203 8 $7,000,000 $4,854,990 9 $7,000,000 $4,637,935 10 $19,000,000 $12,025,869 PVCF $75,601,484

Hence atmost we would pay $75,601,484.

Note that in last year the after tax salvage value is added to cash flow.

If share price increases the PVCF will the discount rate will decrease due to decrease in Ke and hence the PVCFwill increase and hence we will pay more.

If tax rate decreasec the PVCF will increase due to increase in after tax cash flows and hence we will pay more.

If bond sells at par then YTM or cost of debt will increase which will reduce the PVCF and hence we will pay less.