Question

The following table summarizes prices of various default-free zero-coupon bonds (expressed as a percentage of the face value):

Maturity (years)	1	2	3	4	5
Price (per $100 face value)	$96.17	$91.82	$87.19	$82.33	$77.32

a. Compute the yield to maturity for each bond.

b. Plot the zero-coupon yield curve (for the first five years).

c. Is the yield curve upward sloping, downward sloping, or flat?

Answer 1

YTM of Year 1:

Particulars	Amount
Maturity price	$    100.00
Current Price	$      96.17
Maturity period	1

YTM = [ Maturity Value / Current Price ] ^ ( 1 / n ) - 1
= [ $ 100 / $ 96.17 ] ^ ( 1 / 1) - 1
= [ 1.0398 ] ^ ( 1 / 1) - 1
= 1.0398 - 1
= 0.0398
I.e 3.98 %

YTM of Year 2:

Particulars	Amount
Maturity price	$    100.00
Current Price	$      91.82
Maturity period	2

YTM = [ Maturity Value / Current Price ] ^ ( 1 / n ) - 1
= [ $ 100 / $ 91.82 ] ^ ( 1 / 2) - 1
= [ 1.0891 ] ^ ( 1 / 2) - 1
= 1.0436 - 1
= 0.0436
I.e 4.36 %

YTM of Year 3:

Particulars	Amount
Maturity price	$    100.00
Current Price	$      87.19
Maturity period	3

YTM = [ Maturity Value / Current Price ] ^ ( 1 / n ) - 1
= [ $ 100 / $ 87.19 ] ^ ( 1 / 3) - 1
= [ 1.1469 ] ^ ( 1 / 3) - 1
= 1.0468 - 1
= 0.0468
I.e 4.68 %

YTM of Year 4:

Particulars	Amount
Maturity price	$    100.00
Current Price	$      82.33
Maturity period	4

YTM = [ Maturity Value / Current Price ] ^ ( 1 / n ) - 1
= [ $ 100 / $ 82.33 ] ^ ( 1 / 4) - 1
= [ 1.2146 ] ^ ( 1 / 4) - 1
= 1.0498 - 1
= 0.0498
I.e 4.98 %

YTM of Year 5:

Particulars	Amount
Maturity price	$    100.00
Current Price	$      77.32
Maturity period	5

YTM = [ Maturity Value / Current Price ] ^ ( 1 / n ) - 1
= [ $ 100 / $ 77.32 ] ^ ( 1 / 5) - 1
= [ 1.2933 ] ^ ( 1 / 5) - 1
= 1.0528 - 1
= 0.0528
I.e 5.28 %

Part B:

Part C:

Yield Curve is Upward Slopping.