Question

A company that manufactures magnetic membrane switches is investigating three production options that have the estimated cash flows below. Given that the interest rate is 13.9761942% per year compounded continuously, (a) Determine which option is preferable (b) If the options are independent, determine which are economically acceptable (All dollar values are in millions).

	A	B	C
First Cost	-30	-2	0
Annual Cost	-5	-0.2	-2
Annual Income	14	1.5	2.5
Salvage Value	7	-	-
Life,years	10	Infinity	5

Please do not use Excel Function.

Answer 1

Solution :-

Present Worth = Net Annual Cash Inflow * PVAF ( r , n ) + Salvage Value * PVF ( r , n )  - Initial Cost

Present Worth of Option A = ( 14 - 5 ) * PVAF ( 13.976% , 10 ) + 7 * PVF ( 13.976% , 10 ) - 30

= ( 9 * 5.220965 ) + ( 7 * 0.270308 ) - 30

= 46.98869 + 1.892154 - 30

= 18.88084 million

Present Worth of Option B = ( in case of infinity ) = [ Net Annual Cash Inflow / Discount Rate ] - Initial Investment

= [ ( 1.5 - 0.2 ) / 0.13976 ] - 2

= 9.30153 - 2

= 7.30153 million

Present Worth of Option C = ( 2.5 - 2 ) * PVAF ( 13.976% , 5 ) + 0 * PVF ( 13.976% , 5 ) - 0

= ( 0.5 * 3.435046 )

= 1.717523 million

The Options are preferable according to highest , As NPV is higher the better.

Therefore Choose Option A

(ii)

If the options are independent then All options are to be choose as all of the projects has Present Worth Greater than equal to Zero .

PVAF ( 13.976% , 5 ) = [ 1 - ( 1 + 0.13976)^-5 ] / 0.13976

= [ 1 - 0.5199 ] / 0.13976

= 3.435

PVAF ( 13.976% , 10 ) = [ 1 - ( 1 + 0.13976)^-10 ] / 0.13976

= [ 1 - 0.270312 ] / 0.13976

= 5.2209

PVF ( 13.976% , 10 ) = 1 /  ( 1 + 0.13976)¹⁰ = 0.2703

If there is any doubt please ask in comments