Question

On January 1, 2021, Water World issues $24.9 million of 5% bonds, due in 15 years, with interest payable semiannually on June 30 and December 31 each year. Water World intends to use the funds to build the world’s 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. Required: 1-a. If the market rate is 4%, calculate the issue price.

Answer 1

Answer)

Issue of a Bond: The issue price of a bond is aggregate of the present value of coupon payments of the bonds and its redemption value discounted at market rate of interest.

Facts of the question:

Face Value of Bonds = $ 24.90 million or $ 24,900,000

Since coupon is payable semi-annually, the amount of coupon, effective rate of interest (to be used a discounting factor for calculating present value) and the number of periods (to be used a discounting factor for calculating present value) will be as follows:

Since the interest is payable semi-annually, the effective rate of interest will be calculated by dividing the coupon rate of interest divided by 2 (as 2 semi-annual coupon Payments will be made in a year)

Effective rate of coupon interest = coupon rate of interest/ 2

                                             = 5%/2

                                             = 2.50%    

Therefore the effective rate of coupon interest is 2.50%.

Coupon payable = Face value X effective rate of coupon interest

                               = $ 24,900,000 X 2.50%

                               = $ 622,500          

Similarly, Effective market rate of interest to be used as discounting factor in calculation of present value will be:

Effective market rate of interest = market rate of interest/ 2

                                             = 4%/2

                                             = 2.00%    

Therefore the effective market rate interest is 2.00%.

Since coupon will be paid semi-annually number of periods will be:

Number of Semi-annual periods =Number of years X 2

                                                           = 15 years X 2

                                                            = 30 semi-annual payments        

Therefore 30 semi-annual payments will be made over the period of 15 years.

Issue price of bond= Present value of coupon payments + Present value of amount payable on maturity

                                           = $ 622,500 X Present value annuity factor (at 2% rate for 30 periods) + $ 24,900,000 X Present value (at 2% rate at the end of 30 periods)

                                                  = $ 622,500 X 22.396456 + $ 24,900,000 X 0.55207089

                                                  = $ 13,941,794 + $ 13,746,565    

                                                  = $ 27,688,359    

Therefore the issue price of the bonds will be $ 27,688,359.

Note: Since the coupon rate of interest is more than the market rate of interest, bond will be issued at a premium over its face value.