Assignment on Payback Period

QUESTION 1 – For RFN PLC.
(a) Payback period for PROJECT JDS.
Initial cash outflow = ($650,000)
Annual Cash Inflow (Year 1) = $250,000
(Year 2) = $450,000
(Year 3) = $170,000
Using the Subtraction Method;
In year 1, the cash inflow 250,000 can be removed from the initial cost 650,000
completely, and there’d be a remainder of 400,000 on the negative side.
In year 2 however, the cash inflow for the year of 450,000 cannot be removed from the
remainder of 400,000 completely, as there’d be a positive remainder of 50,000.
In light of this, the proportion of cash inflow used to cover the remaining cost of asset
would be found in months. This is done by dividing the cost-remainder by the cash
inflow for the year.
= 400000/450000
= 0.89 years (rounded off to 2 decimal places).
Therefore, the payback period for project JDS using the subtraction method is 1.89 years.
Using the Averaging Method:
Here, the cash inflows for the different years are all added up and averaged over the
number of years for which cash flows are expected. Basically, it’s just the mean of the
annual cash flows. This gives a constant annual cash inflow, which would be used to
divide the initial cost of project JDS to get the payback period.
Annual Cash Inflow = (250,000 + 450,000 + 170,000) / 3 years

= 290,000 per year
Payback Period = Initial Cost of Investment / Annual Cash Inflow
= 650,000 / 290,000
= 2.24 years (rounded off to 2 decimal places)
Therefore, the payback period for project JDS using the averaging method is 2.24 years.
(b) Weighted Average Cost of Capital (W.A.C.C.)
W.A.C.C. = (Weight of Equity Financing to Capital Structure * Cost of Capital) +
(Weight of Debt Financing to Capital Structure * After-tax Cost of Debt) + (Weight of
Preference Share Capital to Capital Structure * Cost of preference share)
For Project JDS – Using Excel Functions
Weight of Debt Financing to Capital Structure 43%
Weight of Equity Financing to Capital Structure 57.00%
After-tax Cost of Debt 9%
Cost of Equity 16%
Weight of Equity Financing * Cost of Equity (A) 9.1200%
Weight of Debt Financing * After-tax Cost of Debt (B) 3.8700%
Weighted Average Cost of Capital (A+B) 12.9900%
The W.A.C.C. computed can be rounded off to the nearest whole number to give 13%
(c) Net Present Value of Project JDS – Using Excel Functions
Yea
r Cash Flows (A) Cost of Capital Discounting Factor (B) Present Value of Cash Flows (A*B)
0 -650,000 0.13 1 -650000
1 250,000 0.13 0.884955752 221238.9381
2 450,000 0.13 0.783146683 352416.0075
3 170,000 0.13 0.693050162 117818.5276
Net Present Value (NPV) 41473.47316
The Net Present Value figure can be rounded off to the nearest whole number to give
$41,473

(d) Internal Rate of Return for Project JDS – Using Excel Functions.
Years Cash Flows (A)
0 -650,000
1 250,000
2 450,000
3 170,000
IRR 0.505727547
The internal rate of return is given as 50.57% when rounded off to 2 decimal places.

QUESTION 2 – For MFN PLC.
(a) W.A.C.C. = (Weight of Equity Financing to Capital Structure * Cost of Capital) +
(Weight of Debt Financing to Capital Structure * After-tax Cost of Debt) + (Weight of
Preference Share Capital to Capital Structure * Cost of preference share).
Market Value of Equity (Ordinary Shares) – 0.75 * 12 million shares - (A) 9,000,000
Market Value of Preference Shares – 0.60 * 5 million shares - (B) 3,000,000
Market Value of Loan Notes – 100 * 1.2 million notes - (C) 12,000,000
Total Market Value of Capital (A+B+C) - (D) 24,000,000
Weight of Equity - A/D 0.375
Weight of Preference Shares - B/D 0.125
Weight of Debt - C/D 0.5
Cost of Equity
Using the Dividend Capitalization Model where R (cost of equity) = (Dividend for the year / Current Market Price) * Dividend growth rate
Dividend per share for the year is the same as earnings for the year since all earnings are distributed as dividends to all shareholders
To get earnings per ordinary share for the year:
Earnings Before Interest and Tax (from income statement) 5,000,000
Less: Interest (9% * 12,000,000) -1080000
Earnings after Interest 3,920,000
Less: Preference Share dividend (7% * 3,000,000) -210,000
Earnings accruable to ordinary shareholders - E 3,710,000
Earnings per share (or dividend per share) - E/12 million shares 0.30916667
Since there is no dividend growth rate, cost of equity can be calculated as the division of dividend for the year by current market price of shares
Cost of Equity - 0.30/0.75 0.4
Cost of Preference Share 0.07
After-tax Cost of Debt (cost of debt) * (1-tax rate) = (0.09) * (1-0.3) 0.063
Weight of Equity * Cost of Equity - F 0.15
Weight of Preference share * Cost of Preference share - G 0.00875
Weight of Debt * After-tax Cost of Debt - H 0.0315
Weighted Average Cost of Capital - F + G + H 0.19025
Relevant Metric

The weighted average cost of capital can be rounded off to the nearest whole number to be 19%
QUESTION 3
(a) To find the amount deposited in a years’ time to be able to withdraw $100,000 in four
years’ time, we’ll use the present value of a one-time lump sum formula. A way to do this
is by recognizing that interest on the amount deposited is only earned for three years, as
opposed to the four year we might assume. The reason for this is that the deposit is only
made at the end of the first year, and the time period between the end of the first year and
the end of the fourth year is three years, so interest is only earned for three years. After
this is recognized, the amount deposited is therefore calculated as follows:
Present Value = Future Value / (1 + Interest rate) ^ number of years
= 100,000 / (1 + 0.08) ^ 3
= 79,383 (rounded off to the nearest whole number)
Therefore, I must pay 79,383 in the bank account one year from now so I can withdraw 100,000
at the end of the fourth year with the current market interest rate.
(b) For me to make equal instalments over a four year period so I could accumulate a total of
100,000, including interest earned over this period is given as:
Using the Future Value of Annuity formula, I make my computations as follows:
Future Value = Regular Payments * ([1 + interest rate] ^ number of years - 1) / interest
rate.
Since future value is known to be 100,000, interest rate to be 8%, and time to be 4 years,
we find regular payments as follows:
100,000 = RP * ([1+0.08] ^ 4 – 1) / 0.08

100,000 = 4.506112 RP
RP = 22,192 (to the nearest whole number)
Therefore, I’d need to make an annual deposit of 22,192 to meet the target of 100,000 in
the next four years, given the prevalent market interest rate.
(c) If my father offered to give me the payments calculated in (b) above, or a lump-sum of
75000 in a years’ time, I would first calculate the present value of these amounts using
the relevant discounting factors before I make my decision. The results gotten for both
alternatives would then inform my decision after I must have compared these results
against each other.
Option 1: Yearly deposit of 22,192. To get the present value, we use the annuity formula
for present value since periodic payments occur consistently.
Present Value = Regular Payments * ((1-[1+interest rate] ^ {-number of years})/interest rate)
= 22,192 * ([1 – {1+0.08} ^ -4] / 0.08)
= 73,503 (rounded off to the nearest whole number)
Option 2: Lump-sum deposit of 75,000 in one year’s time. To get the present value, we’ll
discount the normal way using the discount factor of 1 / (1+r) ^ n.
Present Value = Lump sum payment * 1 / (1+r) ^ n
= 75000 * (1 / [1+0.08] ^ 1)
= 69,444 (to the nearest whole number)
Decision: After comparing the results of both options together, I’ll prefer to receive 22,192 every
year for the next four years than to receive 75000 in the next one year. The reason being that the
former option gives me more value, considering the time value of money and the effects of
interest rates over time.

(d) If I only have 75000 now, the interest rate that’ll will earn me an interest of 25,000, after being
compounded annually, so that the amount that I can collect after a four-year period is 100,000 is
gotten with the formula below:
Present Value = Future Value / (1 + Interest rate) ^ number of years
Since we have Present value to be 75,000, future value to be 100,000, the number of
years to be 4, therefore, the interest rate would be gotten as:
75000 = 100000 / (1+r) ^ 4
Cross multiply both sides
75000 (1+r) ^ 4 = 100000
Divide both sides by 75000
(1+r) ^ 4 = 100000 / 75000
(1+r) ^ 4 = 1.25
Find the nth root of both sides, when n=4.
1+r = 1.0573712634
r = 1.0573712634 – 1
r = 0.06 (rounded off to 2 decimal places)
Therefore the rate of interest that’ll make my onetime investment of 75000 to become
100000 in the next four years is 6% rate of interest.
(e) Supposing I can only deposit 18629 every year for the next four years, and I need to get
100,000 at the end of the fourth year, the rate of interest that will need to be prevalent is
gotten using the following annuity formula:
Future Value = Regular Payments * ([1 + interest rate] ^ number of years - 1) / interest
rate.

Since future value is 100,000, regular payments is 18629, number of years is 4, and the
rate of interest is gotten as:
Using Excel Functions:
Solving for Interest Rate
Present Value 0
Future Value 100000
Annual Payment 18629
Years 4
Interest rate 20%
(f) If my dad helps me make a 40000 deposit in a years’ time, and I’m required to make six
semi-annual equal instalments for me to reach my goal of 100,000 in four years’ time,
how much I will need to be depositing semi-annually is calculated thus:
Since Future Value of the investment is known, we will assume that this figure is a
function of the sum of all future values of the deposits that will be made in future times.
When is the deposit made ? How many years can the deposit earn interest? Interest Rate (Semi-annual) Amount of return gotten, in times.
At the end of Year 1 3 0.04 1.265319018
Mid-year of year 2 2.5 0.04 1.216652902
At the end of Year 2 2 0.04 1.16985856
Mid-year of year 3 1.5 0.04 1.124864
At the end of Year 3 1 0.04 1.0816
Mid-year of year 4 0.5 0.04 1.04
At the end of Year 4 0 0.04 1
The deposit made at the end of Year 1 is known to be 40,000, hence we know the future value to be 40000 * 1.265319018 (A) 50612.76074
However, after that, we do not know the value of the equal deposits after that, hence we sum up the returns as (B) 6.632975462
The idea behind this is that, the sum of A and Bx would result in 100000 (where 'x' represents the amount of equal deposits).
Therefore, A+Bx = 100000
If A = 50612.76074, and B = 6.632975462, the equation will be, 50612.76074 + 6.632975462x = 100,000
Using the Excel Function,
Solving for “x” and collecting like terms, we have

6.632975462x = 100,000 – 50612.76074
6.632975462x = 49387.23926
Divide both sides by the coefficient of x
x = 49387.23926 / 6.632975462
x = 7445.7141509021
x = 7446 (rounded off to the nearest whole number)
Therefore, I will need to deposit 7446 semi-annually for three years to reach my target even after
my dad has helped me front 40,000 out of the required amounts.
(g) The effective annual rate applied by the bank in ‘f’ above is given as:
Using Excel formulas,
Frequency
Compounding
Periods Interest rate
Effective Annual
Rate
Semi-annual 2 0.08 0.0816
Therefore, the effective annual rate is 8.16%
Using algebraic formulas,
Effective Annual Rate= Annual Rate (1+2(0.01))
= 0.08(1+0.02)
= 0.08+0.0016
= 0.0816
Therefore, the effective annual rate is 8.16%