The answer is $31.94. Please show steps to get the calculations. puscit varde. (

Question

The answer is $31.94. Please show steps to get the calculations.

puscit varde. (8) Two projects have equal net present values when calculated using a 6% annual effective interest rate. Project 1 requires an investment of $20,000 immediately and will return $8,000 at the end of one year and $15,000 at the end of two years. Project 2 requires investments of $10,000 immediately and SX in two years. It will return $3,000 at the end of one year and $14,000 at the end of three years. Find the difference in the net present values of the two p they are calculated using a 5% annual effective interest rate. rojects if

Explanation / Answer

First, we have to find the value of X by equalising the net present value (NPV) of the two projects.

Net present value = Present value of cash inflows - Present value of cash outflows

Present value (PV) of an amount can be computed as -

PV = Amount / (1 + r)n

where, r = rate of interest, n = no. of years

NPV of project 1 at 6% = (-)$20,000 + [ $8000 / (1 + 0.06)1 ] + [ $15000 / (1 + 0.06)2 ]

or, NPV of project 1 at 6% = (-)$20,000 + $7,547.16981132 + $13,349.9466001 = $897.1164114

NPV of project 2 at 6% = (-)$10,000 + [ $3000 / (1 + 0.06)1 ] - [ X / (1 + 0.06)2 ] + [ $14000 / (1 + 0.06)3 ]

Also, we are given that at 6% -

NPV of project 1 = NPV of project 2

or, $897.1164114 = (-)$10,000 + $2,830.18867924 - [ X / (1.06)2 ] + $11,754.6699623

or, $897.1164114 = $4,584.8586415 - [ X / (1.06)2 ]

or, [ X / (1.06)2 ] = $3,687.7422301

or, X = $3,687.7422301 x (1.06)2 = $4,143.54716973

Now that we have the value of X, we just need to compute the NPVs at 5% and compute the difference.

NPV of project 1 at 5% = (-)$20,000 + [ $8000 / (1 + 0.05)1 ] + [ $15000 / (1 + 0.05)2 ] = $1,224.4897958

NPV of project 2 at 5% = (-)$10,000 + [ $3000 / (1 + 0.05)1 ] - [ $4,143.54716973 / (1 + 0.05)2 ] + [ $14000 / (1 + 0.05)3 ]

or, NPV of project 2 at 5% = $1,192.5498081

Difference = $1,224.4897958 - $1,192.5498081 = $31.9399877 or $31.94

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