Principles of Banking & Finance: Calculation of Annual Payment and Bond Pricing

This text explains the calculation of annual payment and bond pricing in Principles of Banking & Finance. It includes formulas and solved examples for better understanding. The text also mentions the references used for the explanation.

PRINCIPLE OF BANKING & FINANCE
STUDENT ID:
[Pick the date]

Question 1
The determination of the annual payment for discharging the debt can be made using the
following formula (Parrino & Kidwell, 2014).
PVA = PMT (1-(1/(1+r)n))/r
Based on the information provided, PVA = 60% *10,000 = $6,000, i= 8% p.a., n=3
Hence, 6000 = PMT (1-(1/1.083))/0.08
Solving the above, PMT = $2,328.20
The amortisation table is indicated below.
Total interest paid in three years = 480 + 332.14 +172.46 = $ 984.60
Question 2
The given information about the bond is summarised below.
Par value= $ 1,000
Annual coupon payment = (9/100)*1000 = $ 90
Time of maturity = 14 years
Current price = $ 1,120
a) The requisite formula for pricing of bond is indicated below (Brealey, Myers & Allen,
2014)

Based on the information provided, C = $ 90, n=14, M=$1,000, Bond Price = $1,120, i
=YTM
1120 = [90*(1-(1/(1+YTM))14/YTM] + (1000/(1+YTM)14)
The above has been solved using hit and trial considering the fact that since the bond is
trading at a premium, hence YTM would be lower than 9%.
Solving the above, we get YTM = 7.58% p.a.
b) In the given case, the required return is 8.5%. The requisite formula for pricing of bond is
indicated below.
Based on the information provided, C = $ 90, n=14, M=$1,000, i=8.5%
Hence, bond price = [90*(1-(1/1.085)14)/0.085] + [1000/(1.085)14]
Thus, bond price = [90*(1-0.319142)/0.085] + [1000/3.1334]
Further, bond price = (61.277/0.085) + 319.14
Solving the above, we get bond price = $1,040.05
c) From the output obtained in part (b), it is evident that for the investor to obtain a 8.5% rate
of return, the price needs to be $1,040.05. However, as indicated in part (a), the current price
of the bond is $ 1,120 and the YTM is lower than 8%. Therefore, the investor must not make
the investment (Damodaran, 2015).

References
Brealey, R. A., Myers, S. C. & Allen, F. (2014) Principles of corporate finance, 6th ed. New
York: McGraw-Hill Publications
Damodaran, A. (2015). Applied corporate finance: A user’s manual 3rd ed. New York:
Wiley, John & Sons.
Parrino, R. & Kidwell, D. (2014) Fundamentals of Corporate Finance, 3rd ed. London:
Wiley Publications