Calculating Future Cash Flow
Sources must be cited in APA format. Your response should be four (4) pages in length; refer to the "Assignment Format" page for specific format requirements.
Respond to the items below.
Part A
Given the following cash inflow at the end of each year, what is the future value of this cash flow at 6%, 9%, and 15% interest rates at the end of the seventh year?
Year 1 $15,000
Year 2 $20,000
Year 3 $30,000
Years 4 through 6 $0
Year 7 $150,000
Part B
County Ranch Insurance Company wants to offer a guaranteed annuity in units of $500, payable at the end of each year for 25 years. The company has a strong investment record and can consistently earn 7% on its investments after taxes. If the company wants to make 1% on this contract, what price should it set on it? Use 6% as the discount rate. Assume that it is an ordinary annuity and the price is the same as present value.
Part C
A local government is about to run a lottery but does not want to be involved in the payoff if a winner picks an annuity payoff. The government contracts with a trust to pay the lump-sum payout to the trust and have the trust (probably a local bank) pay the annual payments. The first winner of the lottery chooses the annuity and will receive $150,000 a year for the next 25 years. The local government will give the trust $2,000,000 to pay for this annuity. What investment rate must the trust earn to break even on this arrangement?
Part D
Your dream of becoming rich has just come true. You have won the State of Tranquility’s Lottery. The State offers you two payment plans for the $5 million jackpot. You can take annual payments of $250,000 for the next 20 years or $2,867,480 today.
a. If your investment rate over the next 20 years is 8%, which payoff will you choose?
b. If your investment rate over the next 20 years is 5%, which payoff will you choose?
c. At what investment rate will the annuity stream of $250,000 be the same as the lump sum payment of $2,867,480?
MANAGEMENT FINANCE
Student’s Name:
Affiliated Institution:
Date:
Part A
Explanation:
Calculating future cash follows being given different interest rates of 6%, 9%, and 15% for the seven-year of s present cash flows.
Therefore, the formula for calculating future cash flow is given:
Future value = present value * 1+interest rate where n denotes the period, Kagan, J., James, M., & Kazel, M. (2022).
FV = PV1 + in
Where:
FV= future value.
PV= Present value.
i= Interests of given in that period.
n= Number of periods in which payments will be made
Table SEQ Table \* ARABIC 1:Cashflow Generated in Each Period.
YEAR
CASH FLOWS
1
$ 15,000.00
2
$ 20,000.00
3
$ 30,000.00
4
$ 0
5
$ 0
6
$ 0
7
$ 150,000.00
Solutions 1:
Hence future value at 6% interest for all seven years is given by:
Future Vavlue=$15,0001 + 0.061=$ 15,900
20,0001 + 0.062=$ 22,472
30,0001 + 0.063=$ 35730.48
01 + 0.064=$ 0
01 + 0.065=$ 0
01 + 0.066=$ 0
150,000 1 + 0.067=$ 225,544.5
Typically, we are not adding zeros in this example because they have no effect on our results.
Total future value= =$ 15,900 + $ 225,544.5 + $ 22,472 + $ 35730.48
=$ 225,545
Solutions 2:
Future value for 9% is given by:
Future Value=$15,0001 + 0.091=$ 16350
20,0001 + 0.092=$ 23762
30,0001 + 0.093=$ 38850.87
01 + 0.094=$ 0
01 + 0.095=$ 0
01 + 0.096=$ 0
150,000 1 + 0.097=$ 274205.9
Answer:
We will not add zeros in this example because they have no effect on our results.
The total future value=$ 16350 + $ 23762 + $ 38850.87 + $ 274205.9
=$ 339,136
Solutions 3:
Future value for 15% is given by:
FV=$15,0001 + 0.151=$ 17250
20,0001 + 0.152=$ 26450
30,0001 + 0.153=$ 45626.25
01 + 0.154=$ 0
01 + 0.155=$ 0
01 + 0.156=$ 0
150,000 1 + 0.157=$ 399003
In the same case here, we will not add zeros in this example because they have no effect on our results.
Total Future value =$ 17250 + $ 26450 + $ 45626.25 + $ 399003
=$ 509,935
PART B
Explanation:
From the amount charged to the customer, the corporation will gain 7%. It will discount at 6% to make one percent (7 percent - 1 percent). The annuity's present value will be lower than if it were earned at 7%. County Ranch benefits from this differential.
Solution:
Using the formula of present value for an annuity which is given by:
P=PMT *{1-(11+rate n)rate}
P is the current value of an annuity stream.
PMT = Each annuity payment's dollar amount
r=Rate of interest (also known as the discount rate)
n=Number of periods over which payments will be made, as follows:
PMT= $500
n= 25 years
Rate = 0.06
P=$500 *{1-11+0.06 250.06}
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