Question

A corporate bond has a face value of $1,000 and a coupon rate of 5%. The bond matures in 15 years and has a current market price of $950. If the corporation sells more bonds it will incur flotation costs of $25 per bond. If the corporate tax rate is 35%, what is the after-tax cost of debt capital? please show all steps in the calculation.

Answer 1

Solution:-

Ans:- After tax cost of debt = 3.744%

Calculation:-

Years to mature (N)= 15

Coupon rate = 5%

Interest = 1000*5%=$50

Par value = $1000

Market value after flotation cost (PV)= $950-$25= $925

We have to calculate the Yield to maturity of the bond. The YTM can be calculated using hit and trial method.

Note:- We have to find the discount rate whose PV of cash inflows = $925, that will be the YTM of the bond.

We will use hit and trial method

First we take discount rate 6% as discount rate ,

            Price of bond = 50*PVIFA(6%,15)+1000*PVIF(6%,15)

                                    = 50*9.712249+1000*0.417265

                                    =$902.87751

Now we will assume discount rate to be 5.5%.

Price of bond = 50*PVIFA(5.5%,15)+1000*PVIF(5.5%,15)

                                    = 50*10.037581+1000*0.447933

                                    =$949.812095

Now YTM of bond can be calculated as follows

YTM=Lower DR+Difference b/w DRs{[PV of lower DR-PV]/Absolute difference B/w DRs}

Where, DR stands for discount rate

            PV stands for present value

            B/W stands for between.

Now substituting the value

Half yearly YTM = 5.5%+0.5%*(949.81-925)/(949.81-902.88)

            =5.5%+0.26433%                                           

            =5.76%

Hence the YTM = 5.76%

This is the pre tax cost of debt = 5.76%

Now, After tax cost of debt = Pre tax cost of debt*(1-tax)

                                                   = 5.76%*(1-0.35)

                                                    = 3.744%

Please feel free to ask if you have any query in the comment section.

PVIFA and PVIF calculations:-
years	PVF at 6%	PVF at 5.5%
1	0.943396	0.9478673
2	0.889996	0.89845242
3	0.839619	0.85161366
4	0.792094	0.80721674
5	0.747258	0.76513435
6	0.704961	0.72524583
7	0.665057	0.68743681
8	0.627412	0.65159887
9	0.591898	0.61762926
10	0.558395	0.58543058
11	0.526788	0.5549105
12	0.496969	0.52598152
13	0.468839	0.49856068
14	0.442301	0.47256937
15	0.417265	0.44793305
Total	9.712249	10.0375809