Question

4(b) You have an opportunity to buy a bond with a face value of $10,000 and coupon rate of 14%, payable semi-annually. NOTE: Interest per 6-month period is 7% of Face Value (i.e. $10,000x0.07 = $700 per 6-month period). (i) If the bond matures in five years and you can currently buy one for $8,000, what is your IRR for this investment? (ii) If your MARR for this type of investment is 20%, should you buy the bond?

Answer 1

i)

Let the 6-month IRR be i

Coupon amount=C=$700 per 6-month

Face value of bond=FV=$10000

Purchase value=P=$8000

Number of coupons left=n=5*2=10

NPW of investment=-8000+700*(P/A,i,10)+10000*(P/F,i,10)

(We know at NPW at IRR)

First we estimate NPW at i=9%, i=10% and i=11%

First take i=9%

(1+i)" (P/A, i, n)=

1- (P/A, 0.09, 10) = – (1+0.09)0 -= 6.417658 0.09

(P/A,0.09,10)=1/(1+0.09)^10=0.422411

NPW of investment=-8000+700*6.417658+10000*0.422411=$716.47

Now take i=10%

(1+i)" (P/A, i, n)=

$(P/A,0.10,10)=\frac{1-\frac{1}{(1+0.10)^{10}}}{0.10}=6.144567$

(P/A,0.10,10)=1/(1+0.10)^10=0.385543

NPW of investment=-8000+700*6.144567+10000*0.385543=$156.63

Now take i=11%

(1+i)" (P/A, i, n)=

1 - (Ρ/Α, 0.11, 10) =- (1+0.11) 10 0.11 = 5.889232

(P/A,0.11,10)=1/(1+0.10)^10=0.352184

NPW of investment=-8000+700*5.889232+10000*0.352184=-$355.70

We can say that IRR lies between 10% and 11%

Let us try at i=10.5%

(1+i)" (P/A, i, n)=

$(P/A,0.10,105)=\frac{1-\frac{1}{(1+0.105)^{10}}}{0.105}=6.014773$

(P/A,0.09,10)=1/(1+0.105)^10=0.368449

NPW of investment=-8000+700*6.014773+10000*0.368449=-$105.17

We can say that IRR lies between 10% and 10.5%

Let us interpolate

$y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}*(x-x_{1})$

$y-0.10=\frac{0.105-0.10}{-105.17-156.63}*(0-156.63)$

$y-0.10=0.00299$

y=0.10299 or 10.3%

Nominal IRR=10.3%*2=20.6%

b)

MARR is less than Nominal IRR, we should buy the bond.