Unit 5 BONDS
T5.1 Luck Luke
16,34% – When using the equation to calculate the YTM, it is a process of trial and error.
Total bond value = PV of the lump sum + PV of the annuity
R9 500 = R10 000 + 750 x 1 – [1 ÷ (1 + YTM)^12]
(1 + YTM)^12 YTM
We now have to use trial and error and what we know about bond prices and interest rates to
‘guess’ what the YTM could be. We know that the bond is currently selling for less than the
nominal price (trading at a discount). This indicates that the interest rate in the market (YTM)
is more than the coupon rate, which is 15%.
Let’s try a YTM of 16%:
Total bond value = R10 000 + 750 x 1 – [1 ÷ (1 + 0,08)^12]
(1,08)^12 0,08
Total bond value = R3971,14 + R5 652,06 = R9 623,20
The value of R9 623,20 indicates that the YTM is not 16% and needs to be a bit bigger.
This process should be repeated until the correct yield is found. The YTM for this bond is
16,34%. Calculating the YTM using an equation can become a lengthy process.
Using the financial calculator:
Enter 12 −9 500 750 10 000
n i PV PMT FV
i Is the bond selling at a discount or a premium?
Solve
The period rate is for 8,17%makes semi-annual payments. The yield-to-maturity
8,17%, and the bond
is therefore 16,34% (8,17% x 2).
T5.2 Bond Risky
Part a
Bond Risky price change: (R1 000 – R916,84) / R1 000 = 8,32%
Using the equation:
, R1 000 = R1 000 = R708,92
PV of the lump sum: 1,035^10 1,4106
1 – [1 ÷ (1 + 0,035)^10]
PV of the annuity = R25 x 0,035
0,2911
= R25 x 0,035
= R207,93
The total PV of the bond is therefore R708,92+ R207,93 = R916,85
Using the financial calculator:
Enter 10 3,5 25 1 000
n i PV PMT FV
Bond Not-so-risky price change: (R1 000 – R922,21) / R1 000 = 7,78%
Solve for
Using the equation: 916,84
R1 000 = R1 000 = R649,94
PV of the lump sum: 1,09^5 1,5386
1 – [1 ÷ (1 + 0,09)^5]
PV of the annuity = R70 x 0,09
0,35007
= R70 x 0,09
T5.1 Luck Luke
16,34% – When using the equation to calculate the YTM, it is a process of trial and error.
Total bond value = PV of the lump sum + PV of the annuity
R9 500 = R10 000 + 750 x 1 – [1 ÷ (1 + YTM)^12]
(1 + YTM)^12 YTM
We now have to use trial and error and what we know about bond prices and interest rates to
‘guess’ what the YTM could be. We know that the bond is currently selling for less than the
nominal price (trading at a discount). This indicates that the interest rate in the market (YTM)
is more than the coupon rate, which is 15%.
Let’s try a YTM of 16%:
Total bond value = R10 000 + 750 x 1 – [1 ÷ (1 + 0,08)^12]
(1,08)^12 0,08
Total bond value = R3971,14 + R5 652,06 = R9 623,20
The value of R9 623,20 indicates that the YTM is not 16% and needs to be a bit bigger.
This process should be repeated until the correct yield is found. The YTM for this bond is
16,34%. Calculating the YTM using an equation can become a lengthy process.
Using the financial calculator:
Enter 12 −9 500 750 10 000
n i PV PMT FV
i Is the bond selling at a discount or a premium?
Solve
The period rate is for 8,17%makes semi-annual payments. The yield-to-maturity
8,17%, and the bond
is therefore 16,34% (8,17% x 2).
T5.2 Bond Risky
Part a
Bond Risky price change: (R1 000 – R916,84) / R1 000 = 8,32%
Using the equation:
, R1 000 = R1 000 = R708,92
PV of the lump sum: 1,035^10 1,4106
1 – [1 ÷ (1 + 0,035)^10]
PV of the annuity = R25 x 0,035
0,2911
= R25 x 0,035
= R207,93
The total PV of the bond is therefore R708,92+ R207,93 = R916,85
Using the financial calculator:
Enter 10 3,5 25 1 000
n i PV PMT FV
Bond Not-so-risky price change: (R1 000 – R922,21) / R1 000 = 7,78%
Solve for
Using the equation: 916,84
R1 000 = R1 000 = R649,94
PV of the lump sum: 1,09^5 1,5386
1 – [1 ÷ (1 + 0,09)^5]
PV of the annuity = R70 x 0,09
0,35007
= R70 x 0,09
