Consider the following cash flow of company profits. A company earns $3600 in years 1, 2, & 3, from years 4 through 7 the profits increa

Consider the following cash flow of company profits. A company earns $3600 in years 1, 2, & 3, from years 4 through 7 the profits increase by $500 annually. What is the present worth of this cash flow, if the interest rate is 9% and total years analyzed are 7.

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  1. Answer:

    The present worth of cash flow is $22395.51

    Explanation:

    In this type of question we have two parts of the question the first part we are going to get the present value of it which is when the company earns $3600 for the first 3 years with an interest rate of 9%, so we will use the present value annuity formula as the company is earning future cash flows of a present amount that is agreed upon. The present value annuity formula which is Pv1 = C[(1-(1+i)^-n )/i) where:

    Pv1 is the present value of the cash flows for three years.

    C is the annual cash flows for 3 years which is $3600.

    i is the interest rate on the cash flows which is 9%

    n is the number of years in which the cash flows took which is 3 years.

    Now we will substitute this into the above mentioned formula to get the present value of the cash flows that the company gets for the first 3 years:

    Pv1 = $3600[(1-(1+9%)^-3)/9%]

    Pv1 =$9112.66

    Now we will deal with getting the present value of the remaining 4 years in which the profits increased by $500 therefore the cash flows increased to $4100 for the remaining 4 years of the total 7 years of the cash flows. We will use the present value annuity formula that we used above for the first three years which we will substitute as follows:

    Pv2 is the present value of the 4 years cash flow.

    C is the cash flows of profits which is $4100

    i is the interest rate of 9%

    n is the remaining number of years remaining which is 4 years.

    now we substitute:

    Pv2 = $4100[(1-(1+9%)^-4)/9%]

    Pv2 = $13282.85

    now to get the total present value of the profits we will combine both present values to get the present value of the profits in 7 years:

    Present value for 7 years cash flows = Pv1 + Pv2

                                                                 = $9112.66 + $13282.85

                                                                  =$22395.51

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