¶ … Value
A."Suppose your bank account will be worth $15,000.00 in one year. The interest rate (discount rate) that the bank pays is 7%. What is the present value of your bank account today? What would the present value of the account be if the discount rate is only 4%?"
PV at 7%
=$15,000/1.07
=$14,018.69
With a discount rate of 7.00% of the bank account and a span of 1 year, the projected cash flows of my money are worth $0.07 today, and this is less than the initial $15,000.00. The resulting PV of the $15,000 is $14,018.69,
However, PV at 4%
=$15,000/1.04
=$14,423.08.
Interpretation
With a discount rate of 4.00% of my bank account with a span of 1 year, the projected cash flows are worth $0.08 today, which is less than the initial $15,000.00 money in the bank in one year. The resulting PV of the money in the bank in one year will be $14,423.08.
B. "Suppose you have two bank accounts, one called Account A and another Account B. Account A will be worth $6,500.00 in one year. Account B. will be worth $12,600.00 in two years. Both accounts earn 6% interest. What is the present value of each of these accounts?"
Answer
PV of Account A in one year
$6,500.00/1.06
= $6,132.08
PV of Account B. In 2 years
=$12,600/1.06 in the first year
=$11,886.79
In the second year:
=11886.79 / 1.06
=$11,213.96.
C. "Suppose you just inherited a gold mine. This gold mine is believed to have three years worth of gold deposit. Here is how much income this gold mine is projected to bring you each year for the next three years":
Year 1: $49,000,000
Year 2: $61,000,000
Year 3: $85,000,000
"Compute the present value of this stream of income at a discount rate of 7%. Remember, you are calculating the present value for a whole stream of income, i.e. The total value of receiving all three payments (how much you would pay right now to receive these three payments in the future). Your answer should be one number - the present value for this gold mine at a 7% discount rate but you have to show how you got to this number."
Answer
At 7% discount rate, the value of the gold mine is projected as follows:
=$49,000,000 / (1.07) + $61,000,000 / (1.07)2 + $85,000,000 / (1.07)3
= $45,794,392.52 + $53,279,762.42 + $69,385,319.54
=$168,459,474.48.
"Now compute the present value of the income stream from the gold mine at a discount rate of 5%, and at a discount rate of 3%. Compare the present values of the income stream under the three discount rates and write a short paragraph with conclusions from the computations."
Answer
PV of gold mine at 5%
=$49,000,000 / (1.05) + $61,000,000 / (1.05)2 + $85,000,000 / (1.05)3
=46,666,666.66 + 55,328,798.18 + 73,423,817.39
= $175,419,282.2
PV of gold mine at 3%
=$49,000,000 / (1.03) + $61,000,000 / (1.03)2 + $85,000,000 / (1.03)3
=47,572,815.53 + 57,498,350.46 + 77,787,041.05
=$182,858,207
Table 1 Comparison of the Present Value
First Year
Second Year
Third Year
Total
At 7%
$45,794,392.52
$53,279,762.42
$69,385,319.54
$168,459,474.48
At 5%
$46,666,666.66
$55,328,798.18
$73,423,817.39
$175,419,282.2
At 3%
47,572,815.53
57,498,350.46
77,787,041.05
$182,858,207
Comparison of the three discount rates reveals that the total PV of the gold mine at 3% within the three years is the highest with the total present value of $182,858,207. The total PV of 7% is the lowest that valued $168,459,474.48. However, at 5%, the PV is $175,419,282.2. Thus, the PV at the 3% is the best.
Part II
Based on the business plans of Interstate Travel Center, RJ Wagner & Associates Realty and Ice Dreams, the Interstate Travel Center carries the highest risks out of the three companies. The financial statements of the three companies are used to determine a company carrying highest risks out of the three companies. The paper uses the highest discount rate to evaluate which of the three project carrying highest level of risk. To determine which of the three companies carrying the highest risks, it is critical to calculate the net present value of the three companies using a discounted rate. Valuation using discounted rate is a financial strategy to determine the present value of a company using a future cash flow.
Interstate Travel Center
RJ Wagner & Associates Realty
Ice Dreams
Annual discount rate
10%
10%
10%
Initial Cost of Investment
$2,750,000
$60,000
$52,110
Return of First Year
$660,131
$32,750
$14,659
Return of Second Year
$709,578
$45,877
$28,595
Return of Third Year
$726,520
$75,277
$43,315
Cash Flow First Year
$489,669.00
34,747
$5,458
Cash Flow Second Year
$480,600.00
50,555
$20,681
Cash Flow Third Year
485816.00
83,401
$33,715
Net Present Value:
-$1,542,655.49
$76,029.62
-$4,725.83
PV of Expected Cash flows
$1,207,344.51
$136,029.62
$47,384.17
Interstate Travel Center
The Interstate Travel Center Net Present Value is -$1,542,655.49 and PV of Expected Cash flows of Interstate Travel Center are $1,207,344.51.
With a discount rate of 10.00% and a span of 3 years, your projected cash flows are worth $1,207,344.51 today, which is less than the initial $2,750,000.00 paid in order to begin. The resulting NPV of the above project is -$1,542,655.49, which means you will not receive the required return at the end of the project -- pursuing the above project may not be an optimal decision.
RJ Wagner & Associates Realty
Using the ratio analysis to compare the three companies, the Interstate Travel Center net profit margin remain the same year after year. In the first...
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