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natulia [17]
3 years ago
13

Suppose that you just paid $76,000 for a security that will make its first payment to you in 7 years from today. It will continu

e to make equal annual payments every year indefinitely. Find the size of the payments that you will receive from the security if the interest rate is 5%
Business
1 answer:
iogann1982 [59]3 years ago
7 0

Answer:

$5,346.98

Explanation:

Initial cash flow = 76,000

Discount rate = 5%

Suppose the C.F. in the 7th year is x which will flow till perpetuity

Present value of annual cash flow till perpetuity = Annual cash flow / Discount rate

PV at the 7th year = x/0.05

Discount factor = (1 + r)^n

Discount rate = 5%

Years   D. factor   Cash flows

0                 0            76,000

1           0.952381            -

2          0.907029           -

3          0.863838           -

4          0.822702           -

5          0.783526           -

6          0.746215            -

7           0.710681          x/0.05

So, 76000 = 0.710681 *(x/0.05)

76000 / 0.710681  = x / 0.05

x = 76000 / 0.710681 * 0.05

x = 5346.98408990813

x = 5346.98

Hence, if the interest rate is 5%, $5346.98 will be received annually from the 7th year

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1-10            45,100                   6.144                     277,094.40

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Project B

Years Cashflows Discount factor  Present values

0        (350,000)           1                              (350,000)

1           72,500               0.91                   65,975  

2           65,500               0.83                    54,365  

3           73,800                  0.75                    55,350  

4            71,500                  0.68                    48,620  

5           69,800                  0.62                   43,276  

6           75,500             0.56                   42,280  

7           31,000                  0.51                            15,810  

8           47,500                  0.47                           22,325  

9           55,500                  0.42                   23,310  

10           29,200                  0.38                    11,096

Sum of all present values=NPV=32,407

IRR(by using trial and error method=12.4186%

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Based on the given information, the yearly increase in the inflation rate can be computed using the present value formula from an online finance calculator as below.

<h3>Data and Calculations:</h3>

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Thus, the yearly rate of inflation in car prices over the 8 years that Dave bought his new car for $8,400 is <u>5.1%</u>.

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