Question

In this class, we have not gone over required rate of return or implicit value yet. So, please, explain how you solve this and show work.

Jorn Co is in need of approximately $2,000,000 to finance the purchasing of equipment and inventory for a business expansion. They are trying to decide between the three following scenarios: Option 1: Issuing $3,000,000 in 10-year bonds with an annual 4% coupon rate. Similar bonds have a 9% market rate. Option 2: Issuing $1,500,000 in 10-year bonds with an annual 13% coupon rate. Similar bonds have an 8% market rate. Option 3: Issuing a 10-year $5,000,000 zero-interest-bearing note with an implicit rate of 9.5%. Part A. For each scenario, prepare the amortization table for the first 2 full years. Part B. Besides the difference in market rates, what else should Jorn take into consideration when making their decision?

Answer 1

Amounts are in $

Required rate of return = It is the rate of return which the investors want (This is usually given as market rate)

Implicit rate of return = It is the rate which the bond gives to investor. We must equate this rate to market rate and then find the instruments original value (implicit value)

Coupon rate = Periodical interest rate

If we have market rate, we will discount the future coupon payments along with the principal repayment using market rate to today's terms and the resultant amount is the implicit value of the stock (i.e. it can be sold/issued/purchased at that price)

Option 1 :

Face value = 3,000,000

Coupon = 3,000,000 x 4% = 120,000

Term = 10 year

Discounting rate = 9%

Value of bond

= [Annual coupon x PVIFA(9%,10)] + [Face value x PVIF(9%,10)]

= 120,000 x 6.4176577 + 3,000,000 x 0.42241

= 770,119 + 1,267,230

= 2,037,349

Option 2 :

Face value = 1,500,000

Coupon amount = 13% x 1,500,000 = 195,000

Term = 10 years

Market rate = 8% (Discount rate)

Value of bond

= Coupon x PVIFA(8%,10) + Face value x PVIF(8%,10)

= [195,000 x 6.71] + [1,500,000 x 0.46319]

= 1,308,450 + 694,785

= 2,003,235

Option 3 :

Face value = 5,000,000

Zero Coupon bonds do not pay any coupons during its life time, instead they trade in the market or issued at discount and are redeemed at face value resulting in income for the holders

Market rate = 9.5% (Discount rate)

Bond Value

= Face value x PVIF (9.5%,10)

= 5,000,000 x 0.40351

= 2,017,550

Amortization tables

Year Cash paid Interest Discount premium) Corrying ude 962, 651 2,032,349 63,361.41 2, 100, 110.41 69,063.94 2169,79435 120,000 120,000 183361.41 189,063.94 2 2 1 195,000 160,258.8 157479.5 (503,235) 2,003235 (34,74162) 1,968, 493.8 (33,520.5) 1,930,9733 195,000 2 0 1 Tuesday 8 0 csc2aned with caloscanner 191,667,25 209,875.64 2,982, 450 2,017,550 191,667.25 2,209,217.25 209,875.64 2,419,092.89

Note :

PVIFA = Present Value Interest Factor Annuity

PVIF = Present Value Interest Factor

These values are derived from present value tables available online and can also be calculated using calculator

Part B :

Apart from the difference in market rates, Horn company should consider the availability of cash to pay annual coupons, ability to repay the entire bond face value at end of the bond term. Apart from these they also consider issuing costs, future expected market interest rates etc