Question

In: Finance

To raise fund to finance the establishment of surgical mask production lines, MKTV Mall Company Limited’s...

To raise fund to finance the establishment of surgical mask production lines, MKTV Mall Company Limited’s chief financial officer, Wing Cheng (Wing), suggested issuing perpetual bonds with coupon rate of 8.1% and a face value of $1,000 each Coupon is paid annually.
The current market interest rate is 8%. Wing estimates a 0.7 probability that it will fall to 6%., and a 0.3 probability that next year’s interest rate will increase to 10%.
Required:
(a) If MKTV Mall adopts Wing’s suggestion, evaluate the current market value of the perpetual bond given the probabilities of interest rate change.
(b) The chairperson, Andy Siu (Andy), makes additional suggestion of adding a call provision into the bond contract and make them callable in one year. He suggests the call premium is equal to twice the annual coupon. Andy also wants to make the bonds could be issued at par (i.e. $1,000).
Determine what the new coupon rate of the callable bonds should be to achieve what Andy wants. (Assume that the bonds will be called if the interest rates fall.)
(c) Andy wonders if his idea of call provision could create any value. Calculate the value of the call provision for the callable bond proposed in part (b).

Solutions

Expert Solution

a) Expected value of interest rate after one year = 0.7*6%+0.3*10% = 7.2%

So, Expected value of perpetual bond after one year = 81/0.072 = $1125

Current market value of bond = 81/1.08+1125/1.08 = $1116.67

b) Let the coupon rate of the bonds be c% p.a.

Annual coupon = 10* c

If interest rate rises and bonds are not called (probability of 30%)

Value of bond after one year = 10*c/0.1 = 100*c

Current market value of bond = 10*c/1.08+100*c/1.08 =101.85*c

If interest rate falls and bonds are called (probability of 70%)

call premium = 2*10*c = 20*c

Current market value of bond = 10*c/1.08+(1000+20*c)/1.08 =925.93 +27.78*c

Expected value of bond = 0.3*101.85*c + 0.7* (925.93+27.78*c) = 1000

=> 30.5556*c + 19.4444*c +648.14815 = 1000

=>   50*c = 351.85

c = 7.037

So, coupon rate must be 7.037%

c) If there was no call provision (bond could not be called) and the coupon rate was 7.037%

Expected value of perpetual bond after one year = 70.37/0.072 = $977.366

Current market value of bond = 70.37/1.08+977.366/1.08 = $970.13

Thus, value of call provision = value of callable bond - value of bond without call provision

= $1000 - $970.13

=$29.87

jeff jeffy answered 2 years ago
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