In: Finance
The Robinson Corporation has $44 million of bonds outstanding that were issued at a coupon rate of 12.650 percent seven years ago. Interest rates have fallen to 11.750 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 4.40 percent of the total bond value. The underwriting cost on the new issue will be 2.70 percent of the total bond value. The original bond indenture contained a five-year protection against a call, with a call premium of 6 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.
b. Calculate the present value of total outflows.
c. Calculate the present value of total inflows.
d. Calculate the net present value.
a | Computation of the % discount rate. | ||||||||||||
A | Assume par value of each bond | $1,000 | |||||||||||
B=0.027*A | Underwrting cost per bond | $27 | |||||||||||
Pv=A-B | Amount received per bond | $973 | |||||||||||
Nper | Number of years to maturity | 17 | |||||||||||
Pmt=A*0.1175 | Annual coupon payment | $117.50 | |||||||||||
Fv | Amount tobe paid at maturity | $1,000 | |||||||||||
RATE | Yield to maturity | 12.13% | (Using RATE function of excel with Nper=17, Pv=-973, Pmt=117.50, Fv=1000) | ||||||||||
T | Tax Rate | 0.3 | |||||||||||
C=RATE*(1-T) | After tax cost of debt | 8.49% | |||||||||||
Discount Rate | 9% | (Rounded to whole percent) | |||||||||||
b | Present value of total outflows. | ||||||||||||
A | Bond outstanding | $44,000,000 | |||||||||||
B | Call Premium in 8th year | 3% | 6-(2*1.5) | ||||||||||
C=A*B | Amount of Call Premium tobe paid | $1,320,000 | |||||||||||
D=A+C | Bond refund=New Bond issue(Net amount) | $45,320,000 | |||||||||||
E | Par Value of new Bond issue | $46,577,595 | (45320000/(1-0.027) | ||||||||||
Pmt=E*0.1175 | Annual outflow for coupon payment | $5,472,867 | |||||||||||
Nper | Number of years of coupon payment | 17 | |||||||||||
Fv | Payment at maturity | $46,577,595 | |||||||||||
Rate | Discount Rate | 9% | |||||||||||
PV | Present Value of annual coupon plus maturity payment | $57,520,995 | (Using PV function of excel with Nper=17, Rate=9%,Pmt=-5472867, Fv=46577595) | ||||||||||
X | Present Value of total cash outflows | $57,520,995 | |||||||||||
c | Present value of total inflows | ||||||||||||
Outstanding Bond value | $44,000,000 | ||||||||||||
Pmt=0.1265 | Saving in annual coupon payment | $5,566,000 | |||||||||||
Nper | Number of years | 17 | |||||||||||
Fv | Saving in maturity payment | $44,000,000 | |||||||||||
Rate | Discount rate | 9% | |||||||||||
Y | Present Value of total cash inflows | $57,721,072 | (Using PV function of excel with Nper=17, Rate=9%,Pmt=-5566000, Fv=44000000) | ||||||||||
d=Y-X | Net Present value | $200,077 | |||||||||||
Note : Cash flow of Bond Refund and New Bond issue are equal | |||||||||||||
Hence, not incorporated in Present Value Calculation | |||||||||||||