Question

Cost of debt with fees.  Kenny Enterprises will issue a bond with a par value of ​$1 comma 0001,000​, a maturity of twenty​ years, and a coupon rate of 9.69.6​% with semiannual​ payments, and will use an investment bank that charges ​$2525 per bond for its services. What is the cost of debt for Kenny Enterprises at the following market​ prices?

a.  ​$944.93944.93

b.  ​$998.24998.24

Please show work!

Answer 1

Case 1: Calculation of cost of debt in case market price is $944.9394493 or $944.94

We will find out the cost of debt using IRR technique using the hit and trial method

a) Let IRR be 10%

Face Value = $1000

Coupon rate = 4.848% (payments are to be made semi-annually hence we will divide coupon rate of 9.696% by 2)

Yield to maturity = 5% (payments are to be made semi-annually hence we will divide yield to maturity of 10% by 2)

Current market price of bond = $944.9394493 or $944.94

Maturity years = 40 yrs (payments are to be made semi-annually hence we will multiply maturity yrs of 20 by 2)

We know that Net Present Value = Present value of cash inflows - Present values of cash outflows

Hence by IRR we have,

944.94 = (48.48 x (PVAF (5% , 40 yrs) + (1000 x (PVF (5% , 40th yr)

944.94 = (48.48 x 17.16) + (1000 x 0.1420)

Therefore we have,

944.94 = (831.92 + 142)

hence NPV = -28.98

a) Let IRR be 20%

Face Value = $1000

Coupon rate = 4.848% (payments are to be made semi-annually hence we will divide coupon rate of 9.696% by 2)

Yield to maturity = 10% (payments are to be made semi-annually hence we will divide yield to maturity of 20% by 2)

Current market price of bond = $944.9394493 or $944.94

Maturity years = 40 yrs (payments are to be made semi-annually hence we will multiply maturity yrs of 20 by 2)

We know that Net Present Value = Present value of cash inflows - Present values of cash outflows

Hence by IRR we have,

944.94 = (48.48 x (PVAF (10% , 40 yrs) + (1000 x (PVF (10% , 40th yr)

944.94 = (48.48 x 9.779) + (1000 x 0.02209)

Therefore we have,

944.94 = (474.09 + 22.09)

hence NPV = +448.76

Now we will apply the formula as under to find out the IRR

IRR = Lower rate + lower rate NPV / (lower rate NPV - higher rate NPV) x (Higher rate - Lower rate)

IRR = 5% + (28.98) / (-28.98-448.76) x (10% - 5%)

IRR = 5.30% semi-annually or 5.30 x 2 = 10.60 % pa

Hence cost of debt in case 1 is 10.60% pa

Case 2: Calculation of cost of debt in case market price is $998.2499824 or $998.25

We will find out the cost of debt using IRR technique using the hit and trial method

a) Let IRR be 8%

Face Value = $1000

Coupon rate = 4.848% (payments are to be made semi-annually hence we will divide coupon rate of 9.696% by 2)

Yield to maturity = 4% (payments are to be made semi-annually hence we will divide yield to maturity of 8% by 2)

Current market price of bond = $998.2499824 or $998.25

Maturity years = 40 yrs (payments are to be made semi-annually hence we will multiply maturity yrs of 20 by 2)

We know that Net Present Value = Present value of cash inflows - Present values of cash outflows

Hence by IRR we have,

998.25 = (48.48 x (PVAF (4% , 40 yrs) + (1000 x (PVF (4% , 40th yr)

944.94 = (48.48 x 19.79) + (1000 x 0.208)

Therefore we have,

998.25 = (959.42 + 208)

hence NPV = -169.17

a) Let IRR be 20%

Face Value = $1000

Coupon rate = 4.848% (payments are to be made semi-annually hence we will divide coupon rate of 9.696% by 2)

Yield to maturity = 10% (payments are to be made semi-annually hence we will divide yield to maturity of 20% by 2)

Current market price of bond = $998.2499824 or $998.25

Maturity years = 40 yrs (payments are to be made semi-annually hence we will multiply maturity yrs of 20 by 2)

We know that Net Present Value = Present value of cash inflows - Present values of cash outflows

Hence by IRR we have,

998.25 = (48.48 x (PVAF (10% , 40 yrs) + (1000 x (PVF (10% , 40th yr)

998.25 = (48.48 x 9.779) + (1000 x 0.02209)

Therefore we have,

998.25 = (474.09 + 22.09)

hence NPV = +502.07

Now we will apply the formula as under to find out the IRR

IRR = Lower rate + lower rate NPV / (lower rate NPV - higher rate NPV) x (Higher rate - Lower rate)

IRR = 4% + (169.17) / (-169.17-502.07) x (10% - 4%)

IRR = 5.50% semi-annually or 5.50 x 2 = 11 % pa

Hence cost of debt in case 1 is 11% pa