Question

1. A business invests $5000 and initially plans to achieve annual revenue of $1100/YEAR with $200/YEAR expenses (starting at the end of year 1) for ten years. No market value if used for 10 years.

Part A:

Draw a before tax cash flow diagram of the ten-year plan

Part B:

If at the end of year 6, the investment is sold for $1000, calculate the PW, FW, and AW for the before tax cash flow MARR of 12%. Is the investment worth it? And why ?

Part C:

If the investment was used for ten years with no market value, what are the simple payback and the discounted payback periods.

Part D:

What is the IRR if it used for the ten years with no market value? Is it a good investment in this way? If so why?

Answer 1

PART A

​​​​​PART B

PW = -5000 + 1100(P/A,i,n) - 200(P/A,i,n) +1000(P/F,i,n)

PW = -5000 + 1100(P/A,12,6) - 200(P/A,12,6) +1000(P/F,12,6)

Using DCIF Tables

PW = -5000 + 1100(4.1114) - 200(4.1114) +1000(0.5066)

PW = -$793.14

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FW = -5000(F/P,i,n) + 1100(F/A,i,n) - 200(F/A,i,n) + 1000

FW = -5000(F/P,12,6) + 1100(F/A,12,6) - 200(F/A,12,6) + 1000

Using DCIF Tables

FW = -5000(1.9738) + 1100(8.1152) - 200(8.1152) + 1000

FW = -$1565.32

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AW = -5000(A/P,i,n) + 1100 - 200 +1000(A/F,i,n)

AW = -5000(A/P,12,6) + 1100 - 200 +1000(A/F,12,6)

​​​​​​Using DCIF Tables

AW = -5000(0.2432) + 1100 - 200 +1000(0.1232)

AW = -$192.8.

PART C

Pay back period = 5000/(1100-200) = 5.55 years

PART D

Present worth of benefits = Present worth of cost

1100(P/A,i,n) = 200(P/A,i,n) + 5000

1100(P/A,i,10) = 200(P/A,i,10) + 5000

(P/A,i,10) = [(1+i)^n - 1]/[i(1+i)^n] = [(1+i)^10 - 1]/[i(1+i)^10]

Using trial and error method

i = 12.41% = 12%