Question

Cost of debt with fees. Kenny Enterprises will issue a bond with a par value of ​$1,000​, a maturity of twenty​ years, and a coupon rate of 11.6​% with semiannual​ payments, and will use an investment bank that charges ​$30 per bond for its services. What is the cost of debt for Kenny Enterprises at the following market​ prices? (ROUND TO TWO DECIMAL PLACES.)

a. ​$954.14 = ____%?

b. ​$1,017.02 = ____%?

c. 1,057.63 = ____%?

d. ​$1,136.54 = ____%?

Answer 1

Cost of Debt:

The Rate at which PV of Cash Outflows are equal to PV of Cash Net Inflows.

As 30 is charged by investment bank for its services, the same will be deducted from price of bond.

Part A:

Period	Cash Flow	PVF/[email protected]	PV of Cash Flows	PVF/[email protected]	PV of Cash Flows
1-40	$                  58.00	15.0463	$                        872.69	14.1455	$                     820.44
40	$             1,000.00	0.0972	$                          97.22	0.0805	$                       80.54
PV of Cash Inflows	$                        969.91		$                     900.98
PV of Cash Oiutflows	$                        924.14		$                     924.14
NPV	$                          45.77		$                     -23.16

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 0.5%

= 0.06 + [45.77 / 68.93 ] * 0.5%

= 0.06 + [0.66 ] * 0.5%

= 0.06 + [0.0033]

= 0.0633

YTM for 6M = 6.33%

YTM per anum = 6.33% * 12 / 6

= 12.66%

PArt B:

Period	Cash Flow	PVF/[email protected]	PV of Cash Flows	PVF/[email protected]	PV of Cash Flows
1-40	$                  58.00	16.0461	$                        930.68	15.0463	$                     872.69
40	$             1,000.00	0.1175	$                        117.46	0.0972	$                       97.22
PV of Cash Inflows	$                    1,048.14		$                     969.91
PV of Cash Oiutflows	$                        987.02		$                     987.02
NPV	$                          61.12		$                     -17.11

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 0.5%

= 0.055 + [61.12 / 78.23 ] * 0.5%

= 0.055 + [0.78 ] * 0.5%

= 0.055 + [0.0039]

= 0.0589

YTM for 6M = 5.89%

YTM per anum = 5.89% * 12 / 6

= 11.78%

Part C:

Period	Cash Flow	PVF/[email protected]	PV of Cash Flows	PVF/[email protected]	PV of Cash Flows
1-40	$                  58.00	16.0461	$                        930.68	15.0463	$                     872.69
40	$             1,000.00	0.1175	$                        117.46	0.0972	$                       97.22
PV of Cash Inflows	$                    1,048.14		$                     969.91
PV of Cash Oiutflows	$                    1,027.63		$                 1,027.63
NPV	$                          20.51		$                     -57.72

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 0.5%

= 0.055 + [20.51 / 78.23 ] * 0.5%

= 0.055 + [0.26] * 0.5%

= 0.055 + [0.0013]

= 0.0563

YTM for 6M = 5.63%

YTM per anum = 5.63% * 12 / 6

= 11.26%

Part D:

Period	Cash Flow	PVF/[email protected]	PV of Cash Flows	PVF/[email protected]	PV of Cash Flows
1-40	$                  58.00	17.1591	$                        995.23	16.0461	$                     930.68
40	$             1,000.00	0.1420	$                        142.05	0.1175	$                     117.46
PV of Cash Inflows	$                    1,137.27		$                 1,048.14
PV of Cash Oiutflows	$                    1,106.54		$                 1,106.54
NPV	$                          30.73		$                     -58.40

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 0.5%

= 0.05 + [30.73 / 89.13 ] * 0.5%

= 0.05 + [0.34 ] * 0.5%

= 0.05 + [0.0017]

= 0.0517

YTM for 6M = 5.17%

YTM per anum = 5.17% * 12 / 6

= 10.34%

Pls do rate, if the answer is correct and comment, if any further assistance is required.