You have an employee who enjoys motivating and influencing others. He often takes control of a project. This employee is most li
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Answer:
Ans. c) Discounted period is 1.01 years longer than payback period.
Explanation:
Hi, the payback period is the time that takes for the initial invesment to return to the investor (regardless of the time value of money), so we add the cash flow for every period until the result is zero.
The discounted payback period is almost the same, here we do take into account the time value of money. let´s check out the math to this.
Payback period
Period Cash Flow Adding cash flows Coefficient Payback
0 -$50,000.00 -$50,000.00 3
1 $15,000.00 -$35,000.00 1
2 $15,000.00 -$20,000.00 1
3 $20,000.00 $- 1
4 $10,000.00
5 $5,000.00
Payback period = 3
Discount rate 8%
Period Cash Flow Present Value Adding Cash Coefficient
0 -$50,000.00 -$50,000.00 -$50,000.00
1 $15,000.00 $13,888.88 -$36,111.11 1
2 $15,000.00 $12,860.08 -$23,251.03 1
3 $20,000.00 $15,876.64 -$7,374.38 1
4 $10,000.00 $7,350.29 -$24.09 1
5 $5,000.00 $3,402.91 0.01
Discounted payback period = 4.01
The only thing here that needs some further explanation is the 0.01, this is by doing the following calculation.
This is the fraction of the year that will turn those $24.09 in zero (taking into account the cash flow of period 5 which is 3402.91)
So, discounted payback period - Payback period= 4.01 - 3 = 1.01
Best of luck.
Answer:
The value of the initial deposit = $1269
Explanation:
Given - Account balance of 1723.57 the interest rate of the account is 3.4% compounded daily.
To find - If the account was opened 9 years ago, what was the value of the initial deposit
Proof -
We know that,
If the interest rate is compounded n times per year at an annual rate r, the present value of a A dollars payable t years from now is:
Here,
A = 1723.57
r = 3.4% = 0.034
n = 365 (because it is compounded daily )
t = 9
So,
we get
= 1723.57(1.000093151)⁻³²⁸⁵
= 1723.57(0.736396351)
= 1269.23066 ≈ $1269
∴ we get
The value of the initial deposit = $1269