Question

You bought one of Great White Shark Repellant Co.’s 8 percent coupon bonds one year ago for $800. These bonds make annual payments and mature 12 years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 12 percent. If the inflation rate was 3.2 percent over the past year, what was your total real return on investment? Multiple Choice

.90%

7.36%

-8.89%

.80%

.84%

Answer 1

Price of Bond today = PV of CFs from it.

Year	Cash Flow	PVF/ PVAF @12 %	Disc CF
1 - 12	$      80.00	6.1944	$    495.55
12	$ 1,000.00	0.2567	$    256.68
Bond Price			$    752.23

As Coupon Payments are paid periodically with regular intervals, PVAF is used.
Maturity Value is single payment. Hence PVF is used.

What is PVAF & PVF ???
PVAF = Sum [ PVF(r%, n) ]
PVF = 1 / ( 1 + r)^n
Where r is int rate per Anum
Where n is No. of Years

How to Calculate PVAF using Excel ???
+PV(Rate,NPER,-1)
Rate = Disc rate
Nper = No. of Periods

Holding period Yiled = [ Price at end - Price at begining + Coupon ] / Price at the begining

= [ $ 752.23 - $ 800 + $ 80 ] / $ 800

= $ 32.23 / $ 800

= 0.0403 I.e 4.03%

Particulars	Values
Nominal rate	4.03%
Inflation rate	3.20%

Real rate = [ [ 1 + Nominal Rate ] / [ 1 + Inflation rate ] ] - 1
= [ [ 1 + 0.04 ] / [ 1 + 0.03 ] ] - 1
= [ [ 1.0403 ] / [ 1.032 ] ] - 1
= [ 1.008 ] - 1
= 0.008
i.e, Real rate is 0.8 %

Option D is correct.