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Each of the following scenarios is independent. Assume that all cash flows are after-tax cash flows.
a. Colby Hepworth has just invested $400,000 in a book and video store. She expects to receive a cash income of $120,000 per year from the investment.
b. Kylie Sorensen has just invested $1,400,000 in a new biomedical technology. She expects to receive the following cash flows over the next 5 years:_______.
$350,000, $490,000, $700,000, $420,000, and $280,000.
c. Carsen Nabors invested in a project that has a payback period of 4 years. The project brings in $960,000 per year.
d. Rahn Booth invested $1,300,000 in a project that pays him an even amount per year for 5 years. The payback period is 2.5 years.
Required:
1. What is the Payback period for Colby?
2. What is the payback period for Kylie?
3. How much did Carsen invest in the project?
4. How much cash does Rahn receive each year?

Respuesta :

Answer:

1. 3.33 years

2. 2.8 years

3. $3,840,000

4. $520,000

Explanation:

Payback period calculates the amount of time it takes to recover the amount invested in a project from its cumulative cash flows

1. payback period = amount invested / cash flow = $400,000 / $120,000 =  3.33 years

2. Amount invested = $-1,400,000

Amount recovered in year 1 = $-1,400,000 + $350,000 = $-1,050,000

Amount recovered in year 2 = $-1,050,000 + $490,000 = $-560,000

Amount recovered in year 3 = $-560,000 + $700,000 = $140,000

the amount invested is recovered in 2 years + 560,000/ $700,000 = 2.8 years

3. payback period = amount invested / cash flow

 4 = amount invested / $960,000

amount invested = $3,840,000

4. payback period = amount invested / cash flow

2.5 years = $1,300,000 / / cash flow  

Cash flow = $520,000

The payback period is the time you need to recoup the cost of your investment.

What do you mean by Pay-Back Period?

The payback period calculates the amount of time it takes to recover the investment in the project from the cumulative cash flow.

1. Calculation of payback period for Colby:

[tex]\rm\,Payback \; period = \dfrac{Amount \; Invested \;}{Cash \; Flow}\\\\\rm\,Payback \; period = \dfrac{\$400,000}{\$120,000}\\\\\rm\,Payback \; period = 3.33\, years[/tex]

2. Calculation of payback period for Kylie:

[tex]\rm\,Amount \; invested = \$-1,400,000\\\\Amount recovered in year 1 = $-1,400,000 + $350,000 = $-1,050,000\\\\Amount \; recovered \;in \;year \; 2 = \$-1,050,000 + \$490,000 = \$-560,000\\\\Amount \; recovered \; in \; year \; 3 = \$-560,000 + \$700,000 = \$140,000\\\\[/tex]

The amount invested is recovered in 2 years:

[tex]\rm\,Payback \; period = 2 \; years + \dfrac{560,000}{\$700,000} = 2.8 \;years[/tex]

3. Calculation of amount invested by Carsen:

[tex]\rm\,Payback \; period =\frac{ Amount \;invested}{ cash \;flow}\\\\ 4 = \dfrac{\rm\,Amount \,invested }{\$960,000}\\\\Amount\, invested = \$3,840,000[/tex]

4. Calculation of amount of cashflows Rahn will receive each year:

[tex]\rm\,2.5 \;years = \frac{\$1,300,000}{ cash flow}\\\\Cash flow = \$520,000[/tex]

Hence, the payback period is calculated for each case as per the given information.

Learn more about Payback period, refer:

https://brainly.com/question/23149718

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