Question

You bought one of Mastadon Manufacturing Co.’s 7 percent coupon bonds one year ago for $1,045. These bonds make annual payments, mature twelve years from now, and have a par value of $1,000. Suppose you decide to sell your bonds today, when the required return on the bonds is 6 percent. If the inflation rate was 3.2 percent over the past year, what would be your total real return on the investment? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Total real return %

Answer 1

Bond Price:
It refers to the sum of the present values of all likely coupon payments plus the present value of the par value at maturity. There is inverse relation between Bond price and YTM ( Discount rate ) and Direct relation between Cash flow ( Coupon/ maturity Value ) and bond Price.

Price of Bond = PV of CFs from it.

Year	Cash Flow	PVF/ PVAF @6 %	Disc CF
1 - 12	$                   70.00	8.3838	$                 586.87
12	$             1,000.00	0.4970	$                 496.97
Bond Price			$             1,083.84

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

Realized Ret = [ Bond Price Today - Bond Price one Year ago + COupon ] / Bond Price one Year ago

= [ $ 1083.84 - $ 1045 + $ 70 ] / $ 1045

= $ 108.84 / $ 1045

= 0.1041 I.e 10.41%

Real Ret:

Particulars	Values
Nominal rate	10.41%
Inflation rate	3.20%

Real rate = [ [ 1 + Nominal Rate ] / [ 1 + Inflation rate ] ] - 1
= [ [ 1 + 0.1 ] / [ 1 + 0.03 ] ] - 1
= [ [ 1.1041 ] / [ 1.032 ] ] - 1
= [ 1.0699 ] - 1
= 0.0699
i.e, Real rate is 6.99 %