Corporate Finance Basics: Mortgage, Investment, and Bond Analysis

This assignment delves into fundamental corporate finance concepts. Question 1 focuses on mortgage calculations, determining the mortgage payment and creating a payment schedule over 20 years. Question 2 explores investment returns, calculating the future value of an investment over different time horizons and the annuity payments from a principal amount. Question 3 addresses stock valuation, calculating the present value of a share based on dividends, and projecting dividend growth rates. Finally, Question 4 analyzes bond valuation, determining the price of a coupon-bearing bond, calculating yield to maturity, and evaluating the future value of an annuity based on market discount rates, as well as analyzing a zero-coupon bond.

Corporate Finance -
Basics

Table of Contents
Question 1: ......................................................................................................................................3
Question 2. ......................................................................................................................................4
Question 3: ......................................................................................................................................5
Question 4: ......................................................................................................................................5

Question 1:
Solution:
a) Mortgage Payment can be calculated by using below formula:-
M = P r ( 1 + rn ) / ( 1 + rn ) – 1
Here, P = loan amount = £100,000
n = number of years = 20 years
r = rate of interest = 5% annually
therefore,
Mortgage payment (PMT) = P r ( 1 + r)n / ( 1 + r)n – 1
= 100000 x 0.05 (1 + 0.05)20 / (1 + 0.05)20 – 1
= £8,024.26
b) A table for each year balance of mortgage-
Mortgage Payment (PMT) = P r ( 1 + r)n / ( 1 + r)n – 1
For first year, PMT = 100000 x 0.05 (1 + 0.05)1 / (1 + 0.05)1 – 1
= 5000 (1.05) / (1.05 – 1)
= 5000 x 1.05 / 0.05
= £105,000
For second year, PMT = 100000 x 0.05 (1 + 0.05)2 / (1 + 0.05)2 – 1
= 5000 (1.05)2 / (1.05)2– 1
= 5000 x 1.0025 / 0.1025
= £53,780.49
Therefore,
Number of year Mortgage amount (£)
1 105,000
2 53,780.49
3 36,720.86
4 28,201.18
5 23,097.48
6 19,701.75
7 17,281.98

8 15,472.18
9 14,069.01
10 12,950.46
11 12,038.89
12 11,282.54
13 10,645.58
14 10,102.40
15 9634.23
16 9226.99
17 8869.91
18 8554.62
19 8274.50
20 8024.26
c)
First payment amount = 105,000
Fraction of first payment on mortgage = 105000 – 100000 / 100000
= 5000 / 100000
= 0.5% or ½ %
d)
Fraction of last payment on mortgage = 100000 – 8024.26 / 100000
= 0.9% or 9/10
Question 2.
a) Investment amount = £10,000, Rate of interest = 8% per year, T = 40 years
Amount = P (1 + R% )T
= 10000 (1 + 0.08 )40
= 10000 (1.08)40
= 2,100,000 (approximate)
b) If T = 30 years then amount of retirement money will be
Amount = P (1 + R% )T

= 10000 (1 + 0.08 )30
= 10000 (1.08)30
= £1,000,000 (approximate)
c) Annual income receives from annuity
Principal = £10,000
Duration = 15 years
Then, amount will be-
Annuity Payment (p) = P R (1 + R)N / R( 1 + R)N – 1
= 10000 x 0.08 (1 + 0.08)15 / 0.08 (1 + 0.08)15 – 1
= £855,947.87
Question 3:
a) Market discount rate = 10%, Dividend to be paid in the next year = £1.5 per share
Present Value of MVC's Share = Dividend Payment / Discount Rate
PV of MVC's Share = £1.5 / 0.10
PV of MVC's Share = £15
b) If the dividends are projected to grow at a constant rate forever and the dividend yield is
currently 7.5%, the projected dividend growth rate is:
P = D1 / (R-g)
15 = 1.5/ (0.075-g)
15*(0.075-g) = £1.5
0.075-g = £1.5/£15
0.075 – g = 0.10
g = 0.075 – 0.10
g = -0.025 or -2.5%
c)
Value of Stock = DPS / (Dividend Yield – growth)
= £1.5 / (7.5% – (-2.5%))
= £1.5 / (7.5% + 2.5%)
= £1.5/0.10
= £15
d)

Value of MVC Shares = £15/2 = £7.5
Growth Rate = -2.5%
Number of Years expected to survive at the rate of -2.5% = 7.5/2.5 = 3 years.
Question 4:
a) face value of a bond = £100
market interest rate = 5% / 2 = 2.5% semi-annually
time = 3 years for maturity of bond
semi-annual interest payment = 5% x 100 / 2
= £10
Therefore, interest payment = £20
A coupon bearing bond can be calculated by-
Here, C = periodic coupon payment
F = face value
t = time
T = total number of periods
Therefore, P = 5/ (1.05)1 + 5/ (1.05)2 +105/ (1.05)3
= 4.76 + 4.5 + 91
= 100.26 approx.
b) Yield To Maturity:
YTM = (C + (F-P)/n)
[(F+P)/2]
YTM = (0.05*(100))+((100-102.8)/2)
(100+102.8)/2
YTM = (5+ (-2.8/2))
202.8/2
YTM = (5-1.4)
101.4
YTM = (3.6)/101.4

YTM = 0.036
YTM = 3.6%
c) If Correct market discount rate for each individual payment made by the bond = yield-to-
maturity, the value of an annuity paying £100 every six months for the next three years is as
follows:
Annual Periodic Payments (P) = £100*2 = £200
Number of years (n) = 3
Market Discount Rate (r) = YTM = 3.6%
Future Value of Annuity = [P* (((1+r)n – 1))/ r)]
FV = [£200*(((1+0.036)3 – 1)/0.036)]
FV = [£200*(((1.036)3 – 1)/0.036)]
FV = [£200*((1.112– 1)/0.036)]
FV = [£200*(0.112/0.036)]
FV = [£200*(0.112/0.036)]
FV = [£200*3.11]
FV = £622.22
d) Price of the bond = £102.8
Coupon Rate = 5%
On the same day, a Zero-Coupon Bond of:
Face Value = £100
Years to Maturity = 3 years
Purchase Price = £86.23
Annual Periodic Payments (P) = £100*2 = £200
Number of years (n) = 3
YTM = (C + (F-P)/n)
[(F+P)/2]
YTM = (0)+((100-102.8)/2)
(100+102.8)/2
YTM = (0+ (-2.8/2))
202.8/2
YTM = (0-1.4)

101.4
YTM = -1.4/101.4
YTM =−0.0138
YTM = -1.38%
Market Discount Rate (r) = YTM =−0.0138
Future Value of Annuity = [P* (((1+r)n – 1))/ r)]
FV = [£200*(((1−0.0138)3 – 1)/(−0.0138)]
FV = [£200*(((0.9862– 1)/(-0.0138)]
FV = [£200*((-0.0138)/(-0.0138)])
FV = [£200*(1)]
FV = £200