Question

Elena buys a Canadian 30 year annual coupon bond in the primary market for $1000. The bond has a yield to maturity that reflects a world risk free rate of 4% and a Canadian risk premium of 6%. Immediately before her 4^th coupon payment, she decides to sell the bond in the secondary market. At the time of sale, the world economy is growing and Canada is the G7 country showing the strongest growth. The world risk free rate has fallen to 2% and the Canadian risk premium has fallen to 1%.

Note: You have to show your work here. Without showing the exact equation you used to solve this problem, you will not get any marks!

a) Show the cash flow diagram for the bond, where time zero is the time of the bond sale in the secondary market. This cash-flow diagram should be from the perspective of the new buyer: downward arrows signify cash outflows (payments) and upward arrows signify cash inflows (future receipts). Note: you are being marked on following the instructions.

b) What is the competitive market value of the bond in the secondary market?

c) To simplify the calculation, ignore the coupons Elena has received and only pay attention to the initial bond purchase and final selling price. Calculate Elena’s annual rate of return in the simplified bond?

Answer 1

Notes/ Working

I.) To calculate the market risk premium as the yielding value of the bond the formula is:-

Yielding Rate = Rf+(Rm-Rf)

where Rf= Risk Free Rate

Rm-Rf= Market Risk Premium

Market value of Bond of the Bond will be calculated by formula as under:-

kd= Coupon Rate(1-t)+(MV-FV/n)/(MV+FV/2)

where coupon rate assume to be 10% as the base on FV $1000 being not mention in the question

II.) Curent Market Value of the bond is based on the security risk which is comparitively high as Rf< (Rm-Rf), therefore we assume that the =1

Yield to matuirty = 4%+ 1*6% =10%

Current Bond Value= 10%= (100+MV-1000/30)/MV+1000/2

MV =1000

III.) Now, as the growth of the market is increasing and the risk is decreasing, therefore is affects the value and risk of securities is low therefore, we assume is to be zero

yield to maturity= 2%+ 0* 1%= 2%

Market Value in the secondary market = 2% = 100+(MV-1000/30)/(MV+1000)/2

=1428.57

Now,

a)Cash Flow Diagram for the bond, where time zero is the time of bond sale in the secondary market

Bond ( Perspective of New Buyer)

Time Zero After 30 years of Maturity of Coupon Bond (this right arrow depicts an upward arrow signifying receipts or cash inflow as the upward arrow option is not available in the icons available)

b) The competitive market value in the secondary marlet is Rs.1428.57 (as calculated in the Part III. of Notes/ Working)

c) Initial Bond Price = $1000

Final Selling Price = $ 1428.57

Annual rate of return = (Final Price- Initial Price/ Initial Price)*(1/ total number of years invested)*100

As the coupon bond was selled before 4th year of payment, assume that total year of investment is 3 years thereby dividing the return by 3 to get annual rate of return.

Annual Rate of Return = (1428.57-1000/1000)* (1/3)*100

= 14.29% p.a.