Question

Net Present Value—Unequal Lives Project 1 requires an original investment of $78,300. The project will yield cash flows of $14,000 per year for nine years. Project 2 has a calculated net present value of $18,100 over a seven-year life. Project 1 could be sold at the end of seven years for a price of $51,000. Use the Present Value of $1 at Compound Interest and the Present Value of an Annuity of $1 at Compound Interest tables shown below. Present Value of $1 at Compound Interest Year 6% 10% 12% 15% 20% 1 0.943 0.909 0.893 0.870 0.833 2 0.890 0.826 0.797 0.756 0.694 3 0.840 0.751 0.712 0.658 0.579 4 0.792 0.683 0.636 0.572 0.482 5 0.747 0.621 0.567 0.497 0.402 6 0.705 0.564 0.507 0.432 0.335 7 0.665 0.513 0.452 0.376 0.279 8 0.627 0.467 0.404 0.327 0.233 9 0.592 0.424 0.361 0.284 0.194 10 0.558 0.386 0.322 0.247 0.162 Present Value of an Annuity of $1 at Compound Interest Year 6% 10% 12% 15% 20% 1 0.943 0.909 0.893 0.870 0.833 2 1.833 1.736 1.690 1.626 1.528 3 2.673 2.487 2.402 2.283 2.106 4 3.465 3.170 3.037 2.855 2.589 5 4.212 3.791 3.605 3.352 2.991 6 4.917 4.355 4.111 3.784 3.326 7 5.582 4.868 4.564 4.160 3.605 8 6.210 5.335 4.968 4.487 3.837 9 6.802 5.759 5.328 4.772 4.031 10 7.360 6.145 5.650 5.019 4.192 a. Determine the net present value of Project 1 over a seven-year life with residual value, assuming a minimum rate of return of 10%. If required, round to the nearest dollar. $ b. Which project provides the greatest net present value?

Answer 1

Project 1:
Present Value of annual cash flows				$     14,000	x	4.868	=	$   68,152
Present value of salvage value				$     51,000	x	0.513	=	$   26,163
Total Present value of cash flow								$   94,315
Less:Initial Investment								$   78,300
Net Present Value								$   16,015
Thus,
a.	Net present value of Project 1 over a seven-year life with residual value							$   16,015
b.	Over 7 years			Project 2
	Working:
			Net Present Value
	Project 1		$ 16,015
	Project 2		$ 18,100
	Over 9 years			Project 1
	Working:
			Net Present Value
i.	Project 1		$ 23,950
	Project 2		$ 18,100
ii.	Present Value of annual cash flows				$ 14,000	x	5.759	=	$   80,626
	Present value of salvage value				$ 51,000	x	0.424	=	$   21,624
	Total Present value of cash flow								$1,02,250
	Less:Initial Investment								$   78,300
	Net Present Value								$   23,950