Question

The Robinson Corporation has $39 million of bonds outstanding that were issued at a coupon rate of 12.150 percent seven years ago. Interest rates have fallen to 11.150 percent. Mr. Brooks, the Vice-President of Finance, does not expect rates to fall any further. The bonds have 17 years left to maturity, and Mr. Brooks would like to refund the bonds with a new issue of equal amount also having 17 years to maturity. The Robinson Corporation has a tax rate of 30 percent. The underwriting cost on the old issue was 3.90 percent of the total bond value. The underwriting cost on the new issue will be 2.40 percent of the total bond value. The original bond indenture contained a five-year protection against a call, with a call premium of 9 percent starting in the sixth year and scheduled to decline by one-half percent each year thereafter. (Consider the bond to be seven years old for purposes of computing the premium.) Use Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. Assume the discount rate is equal to the aftertax cost of new debt rounded up to the nearest whole percent (e.g. 4.06 percent should be rounded up to 5 percent)

a. Compute the discount rate. (Do not round intermediate calculations. Input your answer as a percent rounded up to the nearest whole percent.)
  

b. Calculate the present value of total outflows. (Do not round intermediate calculations and round your answer to 2 decimal places.)
  

c. Calculate the present value of total inflows. (Do not round intermediate calculations and round your answer to 2 decimal places.)
   

d. Calculate the net present value. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.)
  

Answer 1

a. Compute the discount rate. (Do not round intermediate calculations. Input your answer as a percent rounded up to the nearest whole percent.)

Characteristics of new bond:

Face Value, FV = $ 39 mn = $ 39,000,000

Annual payment = Coupon = 11.150% = 11.15% x 39,000,000 =  $ 4,348,500

Market value, PV = FV - Underwriting cost = 39,000,000 x (1 - 2.4%) = $ 38,064,000

Period = 17 years

Yield to maturity = y = RATE(Period, payment, PV, FV) = RATE(17, 4348500, 38064000, 39000000) = 11.48%

Tax rate = T = 30%

After tax cost of new debt = y x (1 - T) = 11.48% x (1 - 30%) = 8.03%  = 9% (rounded up to the nearest whole percent)

Discount rate, R = 9%

Please enter your answer as 9%.

b. Calculate the present value of total outflows. (Do not round intermediate calculations and round your answer to 2 decimal places.)
Outflows comprise of following:

1. At t = 0, Post tax call premium on old bond = Call premium rate x FV x (1 - T) = (9% - 1.5%) x 39,000,000 x (1 - 30%) =  2,047,500
2. At t= 0, New bond underwriting cost = 2.4% x FV = 2.4% x 39,000,000 =  936,000
3. Annual net tax savings lost on amortization of underwriting cost = (Annual amortization expense of old bond issue - Annual amortization expenses of new bond issue) x Tax rate = (3.9% / 24 - 2.4% / 17) x 39,000,000 x 30% = $  2,494.85 = A . This is an annuity over N = 17 years. PV of this annuity = A / R x [1 - (1 + R)^-N] = 2,494.85 / 9% x [1 - (1 + 9%)^-17] = $  21,315.10

Hence NPV of outflows =  2,047,500 + 936,000 + PV of annuity of $ 2,494.85 over 17 years = $  2,983,500.00 + $ 21,315.10 = $ 3,004,815.10

c. Calculate the present value of total inflows. (Do not round intermediate calculations and round your answer to 2 decimal places.)
Inflows comprise of following:

1. At t = 0, Tax benefit due to expensing the balance underwriting cost from the old bond = Balance underwriting cost to be expensed x Tax rate = $ 39,000,000 x 3.9% x 17 / (7 + 17) x 30% =  $ 323,212.50
2. Annual post tax, net interest saved = (Old coupon rate - New coupon rate) x FV x (1 - T) = (12.15% - 11.15%) x 39,000,000 x (1 - 30%) = $  273,000 = A . This saving is in annuity over N = 17 years. NPV of this annuity = A / R x [1 - (1 + R)^(-N)] = 273,000 / 9% x [1 - (1 + 9%)^-17] = $  2,332,411.36

Hence, NPV of inflows = $ 323,212.50 + $  2,332,411.36 = $ 2,655,623.86

d. Calculate the net present value. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.)

NPV = NPV of Inflows - NPV of outflows = $ 2,655,623.86 - $ 3,004,815.10 = - $ 349,191.24