Question

A 6% annual coupon bond has 11 years remaining until maturity. Par value is $1000.

The required rate of return (yield to maturity)on the bond is 8.5%.

Compute the price of the bond today using the appropriate Excel formula

Compute the price of the same bond if it has 10 years remaining to maturity instead of 11.

What is the capital gains yield on the bond?

What is the current yield on the bond?

What is the total yield on the bond?

What will the bond's price be at the instant before it matures?

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.

Part A:

Year	Cash Flow	PVF/ PVAF @8.5 %	Disc CF
1 - 11	$                   60.00	6.9690	$                 418.14
11	$             1,000.00	0.4076	$                 407.64
Bond Price			$                 825.78

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

Part B:

Year	Cash Flow	PVF/ PVAF @8.5 %	Disc CF
1 - 10	$                   60.00	6.5613	$                 393.68
10	$             1,000.00	0.4423	$                 442.29
Bond Price			$                 835.97

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

Part C:

Total Yield:

YTM :

It is already given as 8.5%.

Part D:

Current yield = Coupon Amount / Price

= $ 60 / $ 825.78

= 0.0727 I.e 7.27%

Part E:

Capital gain yield = Total Yield - Current Yield

= 8.5% - 7.27%

= 1.23%

Part F:

Before Maturity Price of Bond = Coupon Amount + Maturity Value

= $ 60 + $ 1000

= $ 1060