Financial Management Assignment: Annuity, Valuation, and Bond Pricing

This financial management assignment solution addresses several key concepts in finance. It begins with an annuity calculation to determine the annual savings required for a student to purchase a car, considering present and future values. The solution then analyzes loan repayment terms, comparing the impact of different installment amounts on the repayment period. Furthermore, the assignment delves into the valuation of lottery proceeds, treating them as an annuity due and calculating their present value. The solution also covers retirement planning, determining the annual investment needed to meet retirement goals, considering future value calculations. Finally, the assignment presents a valuation of different contract offers based on present value, allowing for the selection of the most favorable offer. The solution also covers stock valuation using the dividend discount model, and bond pricing calculations.

FINANCIAL MANAGEMENT
STUDENT ID:
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Question 2
a) The car would cost $ 15,000 after 4 years.
Price of car in present value terms = 15000/(1.044) = $12,822.06
Current savings that Polly has = $ 3,000
Shortfall in present value terms = $12,822.06 - $ 3,000 = $9,822.06
The above amount should be present value of the incremental savings that Polly needs to
do through annuity. The relevant formula for PV of annuity is indicated below.
In the given case, r =4% and n = 4
Hence, $9,822.06 = P*(1-1.04-4)/0.04
Solving the above, we get P = $ 2,705.88
Thus, Polly needs to make an annual saving of $ 2,705.88 to buy the car.
b) The computation of the loan amount is based on the given information.

Now, if the quarterly instalment is increased to $3,876, then the repayment time is computed
as shown below.
It is evident from the above that higher instalment amount would lead to loan being paid back
one year earlier.
(c) This is an example of annuity due as the first payment is received today. The present
value of annuity due can be estimated using the formula listed below.
In the given case, P = $80,000, r=5% and n=10
Hence, PV of lottery proceeds = 80000 + 80000*(1-1.05-9)/0.05 = $648,625.7
Thus, the present value of the cash flows received from the lottery is $648,625.7.

Question 3
(a)It is known that during retirement a yearly cash flow of $ 80,000 would be required for 25
years. The present value of the above annuity at 8% discount rate would give an estimate
of the amount required at the time of retirement. The relevant formula for PV of annuity is
indicated below.
In the given case, P=$80,000, r=8%, n=25
Hence, PV of annuity = 80000*(1-1.08-25)/0.08 = $853,982.1
The above amount should be with Derek when he retires 20 years later.
FV of the current accumulated amount of $ 40,000 at the end of 20 years = 40000*1.0820 =
$186,438.3
Hence, shortfall expected in the retirement account = $853,982.1 - $186,438.3 = $667,543.8
The above amount is the FV of the investment that Derek needs to do in 20 years leading to
retirement. The relevant formula for FV of annuity is given below.
In the given case, FV = $667,543.8, r=8% and n =20
Hence, $667,543.8 = P*(1.0820-1)/0.08
Solving the above, we get P = $14,587.31

Therefore, Derek needs to deposit $14,587.31 on an annual basis for the next 20 years to
achieve his retirement goal.
(b) In order to estimate the best offer, the present value of the future cash flows needs to be
estimated which is carried out below.
Present Value of Existing Contract = (815000/1.1) + (367500/1.12) + (274000/1.13) +
(184725/1.14) + (184725/1.15) = $ 1,491,358
Present Value of Team’s Offer = (402500/1.1) + (385000/1.12) + (385000/1.13) +
(395000/1.14) + (395000/1.15) = $ 1,488,401
Present Value of Josh’s Offer = (527500/1.1) + (757500/1.12) + (365000/1.13) +
(282500/1.14) + (252500/1.15) = $ 1,729,542
From the above computation, it is apparent that Josh’s offer has the highest offer in present
terms and hence it should be the preferred option from the available three options.
Question 4
(a)The relevant formula to be used is given below.
Current Price of Share (P0)= [ Current Dividend (D0) x (1+growth rate)] / (Required rate of
return-growth rate)
Based on the given data, current dividend = $ 3.36, growth rate = 6.5%, required rate of
return = 12%
Hence, price of share for AVA = (3.36*1.065)/(0.12-0.065) = $ 65.06
(b)The relevant formula to be used is given below.
Current Price of Share (P0)= [Next year dividend ] / (Required rate of return-growth rate)
Based on the given data, Current share price = $25.25, Next year dividend = $1.6, growth rate
= 8.5%

Hence, 25.25 = 1.6/ (Required rate of return- 0.085)
Solving the above, required rate of return = 14.84%
(c) The bond price can be estimated using the following formula.
In the given case, C = 5% of 1000 = $50, i=(11.28/2)% = 5.64%, M = $1,000, n=8*2=16
Hence, bond price = 50*[(1-(1/1.056416))/0.0564] + 1000/(1.056416) = $ 933.69
The company intends to raise $ 2,800.000 from the issuance of bonds. The number of bonds
required to be issued is computed below.
Bonds required for capital investment = ($ 2,800.000/$ 933.69) = 3000 (round to closest
‘000)