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Svet_ta [14]
3 years ago
14

Martha receives $200 on the first of each month. Stewart receives $200 on the last day of each month. Both Martha and Stewart wi

ll receive payments for 30 years. The discount rate is 9 percent, compounded monthly. What is the difference in the present value of these two sets of payments?
Business
1 answer:
Mekhanik [1.2K]3 years ago
3 0

Answer:

Instructions are below.

Explanation:

Giving the following information:

Martha receives $200 on the first of each month. Stewart receives $200 on the last day of each month. Both Martha and Stewart will receive payments for 30 years. The discount rate is 9 percent, compounded monthly.

To calculate the present value, first, we need to determine the final value.

i= 0.09/12= 0.0075

n= 30*12= 360

<u>Martha:</u>

FV= {A*[(1+i)^n-1]}/i + {[A*(1+i)^n]-A}

A= montlhy payment

FV= {200*[(1.0075^360)-1]}/0.0075 + {[200*(1.0075^360)]-200}

FV= 366,148.70 + 2,746.12

FV= 368,894.82

Now, the present value:

PV= FV/ (1+i)^n

PV= 368,894.82/ 1.0075^360

PV= $25,042.80

<u>Stewart:</u>

FV= {A*[(1+i)^n-1]}/i

A= monthly payment

FV= {200*[(1.0075^360)-1]}/0.0075

FV= 366,148.70

PV= 366,148.70/1.0075^360

PV= $24,856.37

Martha has a higher present value because the interest gest compounded for one more time.

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2 years ago
If the discount rate is 21% and the steady growth rate after 3 years is 2%, what should the stock price be today
jonny [76]

<u>Complete Question:</u>

Tattletale News Corp. has been growing at a rate of 20% per year, and you expect this growth rate in earnings and dividends to continue for another 3 years.

a. If the last dividend paid was $10, what will the next dividend be? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Dividend  $

b. If the discount rate is 21% and the steady growth rate after 3 years is 2%, what should the stock price be today? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Stock price  $

Answer:

Requirement A. $12 per share

Requirement B. $44.14 per share

Explanation:

Requirement A.

The next dividend can be calculated using the following equation:

Next Dividend = D0 * (1 + g)

Here

D0 is the current dividend which is $10 and g is the Growth Rate which is 20% for the first three years

By putting values, we have:

Next Dividend = $10 * (1 + 20%)

= $12 per share

Requirement B.

Year  Dividend  Growth Rate  New Dividend

1               10                      20%           12

2               12                      20%                 14.40

3                 14.4                     20%         17.28

4            17.28                    2%                   17.63

Stock Price = $17.63 * (1 + 2%) / (21% - 2%) = $94.62

The above stock price calculated is the value of stock at the end of year 4. To discount it back to year zero, we will discount it by 21%.

Stock price at year0 = $94.62 / (1 + 21%)^4 = $44.14 per share

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Answer:

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P/YR = 12

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