None of the projects generate any additional benefits after Year 4. Assume that

Question

None of the projects generate any additional benefits after Year 4. Assume that the interest rate is and will remain 5% through all of these years and that compounding happens annually. Recall that the formula for the present value (PV) of a future payment (F) that will happen t years from now with an interest rate of r is: None of the projects generate any additional benefits after Year 4. Assume that the interest rate is and will remain 5% through all of these years and that compounding happens annually. Recall that the formula for the present value (PV) of a future payment (F) that will happen t years from now with an interest rate of r is: PV = F/(1 + r)^t a. Fill in the table below with the present value of the each of the future payments given in the table above. For example, the present value of the income from Project A in Year 4 (and only Year 4) is:

Explanation / Answer

a.

b.

c.

If cost of the project is $620 then Project C & Project E would be attractive since only these two projects provide cash inflow in Present value terms more than cash outflow i.e. inflow of $622.8063 - Project C & $623.1251 - Project E resulting in NPV of $2.8063 - Project C & $3.1251 - Project E

d.

Discounting Project A by 4.5%, Project B by 4.6%, Project C by 5.5%, Project D by 4.5%, Project E by 5.5% we get the following present value

Calculation of interest rate that makes present value of future payments exactly equal to $620. For reference project A calculation are as follows

Increase/decrease NPV because of increase/decrease of percentage = $626.102-618.6928 = $7.4091531

Reduction/Increase required = $620-$618.6928 = $1.3072

Decrease/Increase in percent = 4.5% - 5% = -0.5%

Decrease/Increase in percent required = 1.3072*0.5/7.4091531 = -0.0882152

Interest rate to be used that makes the present valueof future payments exactly equal to $620 = 5-0.0882152 = 4.91%

Project A Project B Project C Project D Project E Year 1 190.4762 95.2381 190.4762 47.61905 285.7143 Year 2 181.4059 226.7574 181.4059 226.7574 45.35147 Year 3 0 86.38376 86.38376 215.9594 86.38376 Year 4 246.8107 205.6756 164.5405 123.4054 205.6756

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