Question

What must be the first cost of Alternative B to make the two alternatives equally attractive economically at an interest rate of 8% per year

Answer 1

Answer:

The answer is "21,622.98".

Explanation:

In the given question some information is missing, which can be defined in the given attachment.

To calculate the first cost we first subtract B cost is to X.      

NPV = Cash Flow of the sum of PV amount  

$PV = \frac{Flow of cash} {(1+i)^n} \\\\ \ Calculating \ the \ NPV \ of \ option \ A:$

$= \frac{-16600}{(1 + 0.08)^0}-\frac{2400}{(1 + 0.08)^1}-\frac{2400}{(1 + 0.08)^2} -\frac{2400}{(1 + 0.08)^3}-\frac{2400}{(1 + 0.08)^4}$

$= \frac{-16600}{1}-\frac{2400}{1.08}-\frac{2400}{1.16}-\frac{2400}{1.25}-\frac{2400}{1.36}$

$=-16600-2222.22-2068.96-1920-1764.70\\\\=-24,575.88$

The value of Option A or NPV = -24,575.88

The value of Option B or NPV:

$=-\frac{X}{(1 + 0.80)^0}-\frac{1000}{(1 + 0.08)^1} -\frac{1000}{(1 + 0.08)^2}-\frac{1000}{(1 + 0.08)^3}-\frac{1000}{(1 + 0.08)^4} \\\\ =-\frac{X}{(1.80)^0}-\frac{1000}{(1.08)^1} -\frac{1000}{(1.08)^2}-\frac{1000}{(1.08)^3}-\frac{1000}{(1.08)^4}$

$= -\frac{X}{1}-\frac{1000}{1.08}-\frac{1000}{1.16}-\frac{1000}{1.25}-\frac{1000}{1.36}\\\\= -X -555.55-862.06-800-735.29\\\\=-X -2952.9$

The value of Option B or NPV = -X -2952.9

As demanded  

In Option B  the value of NPV = In Option A  the value of  NPV  

$-X -2952.9= -24,575.88\\\\-X= -21,622.98\\\\X=21,622.98$