Solution
Brijesh answered on
Apr 06 2020
Question 1:
a) Since Sandy would receive these cash-flows in future, “Time-value of money” concept comes in picture here. The maximum amount to be paid for this investment should not be more than “Present Value” of all future cash-flows discounted at the relevant interest rate.
Formula:
Present Value = [(Cash Inflow1)/(1+r)1] + [(Cash Inflow2)/(1+r)2] + [(Cash Inflow3)/(1+r)3]…..+ [(Cash Inflown)/(1+r)n]
Where, “r” is interest rate and “n” is number of years.
Maximum amount to be paid for this investment opportunity
· ($400/1.09) + ($800/1.092) + ($500/1.093) + ($400/1.094) + ($300/1.095)
· ($400/1.09) + ($800/1.1881) + ($500/1.295029) + ($400/1.41158161) + ($300/1.538623955) = $1,904.76
So, Sandy should pay $1,904.76 at most for this investment opportunity.
) The cash-flow stream required here qualifies as “Annuity Due”, since the payment is made at the start of each period. So, to calculate the quarterly payment to pay off the loan in 20 installments, we would need to use below formula.
Formula:
Where,
“Pmt” is periodic payments to payoff loan,
“r” is interest rate = 10%/4 = 2.5% (Since a year has 4 quarters and interest quoted is annual)
and “n” is number of periods = 20 quarterly payments
· Pmt = $100,000*[0.025/(1)-((1+0.025)-20)] * [1/(1+0.025)]
· $100,000 * 0.064147129 * 0.975609756
· $100,000*0.062582565 = $6,258.26
So, Lee has to make quarterly payment of $6,258.26 to pay-off the loan with 20 payments.
c) Since Dianne would start receiving her monthly payments after two years, firstly future value of $200,000 invested today needs to be calculated.
Formula: Future Value = Present Value * (1+r)n
Since the interest is compounded monthly, we would compound the periods as well.
So, r = 0.10/12 = 0.008333333
n = 2 Years * 12 = 24
Future value = $200,000*(1.008333333)24
=> $200,000*1.220390961 = $244,078.19
Now, to calculate monthly payment, we would use “Annuity Due Payments” formula as the first payment is being made at the start of the month.
Formula:
PV = $244,078.19
= 0.008333333
n = 150
Monthly Payments
· $244,078.19*[(0.008333333)/((1)-(1.008333333)-150]*(1/1.008333333)]
· $244,078.19*0.011703999*0.991735538
· $244,078.19*0.011607272 = $2,833.08
So, Dianne will receive $2,833.08 as monthly payments for 150 months.
Question 2:
i) Timeline:
%
8%
6%
7%
Yea
0
1
2
3
4
5
6
7
8
9
10
CFi
$0
$0
$6,500
$1,500
$0
$0
-$2,500
$0
$0
$10,000
$0
ii) In order to determine value of all cash-flows, we would need to determine cu
ent value of funds on a specific timeline. Since there are cash-flows that occu
ed before the timeline and after the timeline, we would need to determine both; Present Value and Future Value. A cash-flow occu
ing after the targeted period would be taken to present value and a cash-flow occu
ing before the targeted period would be taken to future value.
Value at Time1:
Yea
Cash-Flow
Interest Rate
Present Value at Time1
Future Value at Time 1
Value of Cash-flow at Time1
1
$0
8%
$0.00
$0.00
$0.00
2
$6,500
8%
$5,572.70
$0.00
$5,572.70
3
$1,500
6%
$1,259.43
$0.00
$1,259.43
4
$0
6%
$0.00
$0.00
$0.00
5
$0
6%
$0.00
$0.00
$0.00
6
-$2,500
6%
-$1,762.40
$0.00
-$1,762.40
7
$0
6%
$0.00
$0.00
$0.00
8
$0
6%
$0.00
$0.00
$0.00
9
$10,000
7%
$5,439.34
$0.00
$5,439.34
10
$0
7%
$0.00
$0.00
$0.00
Net Value at Time1
$10,509.07
Value at Time5:
Yea
Cash-Flow
Interest Rate
Present Value at Time5
Future Value at Time5
Value of Cash-flow at Time5
1
$0
8%
$0.00
$0.00
$0.00
2
$6,500
8%
$0.00
$8,188.13
$8,188.13
3
$1,500
6%
$0.00
$1,685.40
$1,685.40
4
$0
6%
$0.00
$0.00
$0.00
5
$0
6%
$0.00
$0.00
$0.00
6
-$2,500
6%
-$2,358.49
$0.00
-$2,358.49
7
$0
6%
$0.00
$0.00
$0.00
8
$0
6%
$0.00
$0.00
$0.00
9
$10,000
7%
$7,628.95
$0.00
$7,628.95
10
$0
7%
$0.00
$0.00
$0.00
Net Value at Time5
$15,143.99
Value at Time10:
Yea
Cash-Flow
Interest Rate
Present Value at Time10
Future Value at Time10
Value of Cash-flow at...