Question

On January 1 2021 Water World issues $26 million of 7% bonds, due in 10 years with interest payable semiannually on June 30 and December 31 each year. Water world intends to use the funds to build the worlds largest water avalanche and the tornado- a giant outdoor vortex in which riders spin in progressively smaller and faster circles until they drop through a small tunnel at the bottom.


1-a. If the market rate is 6% calculate the issue price. (FV of $1, PV of $1, FVA of $1, and PVA of $1)

2-a. If the market rate is 7% calculate the issue price

3-a. If the market rate is 8% calculate the issue price

Answer 1

Answer:

See below.

Explanation:

To make the calculations for issue prices we need to identify Net present value of the bonds.

This can be done as follows,

NPV = (Coupon rate of bond * annuity 10 years @ MR) + Par value * PV

where, MR = market rate and PV = present value factor at time of maturity.

1-a)

Annuity factor for 10 years @ 6% market rate = 7.3601

PV factor for 10th year @ 6% market rate = 0.5584

Coupon rate = 26*0.07 = $1.82 million

Issue Price = (1.82 * 7.3601) + 27*0.5584 = $28 million rounded off.

1-b)

Annuity factor for 10 years @ 7% market rate = 7.024

PV factor for 10th year @ 6% market rate = 0.5083

Coupon rate = 26*0.07 = $1.82 million

Issue Price = (1.82 * 7.024) + 27*0.5083 = $26.5 million rounded off.

1-c)

Annuity factor for 10 years @ 8% market rate = 6.710

PV factor for 10th year @ 6% market rate = 0.4632

Coupon rate = 26*0.07 = $1.82 million

Issue Price = (1.82 * 6.710) + 27*0.4632 = $24.7 million rounded off.

Hope that helps.