Question

In: Finance

Consider a firm with a contract to sell an asset for $220,000 seven years from now....

Consider a firm with a contract to sell an asset for $220,000 seven years from now. The asset costs $75,000 to produce today. Given a relevant discount rate on this asset of 7.5 percent per year, will the firm make a profit on this asset? (3 points )At what rate does the firm just break even? (3 points)

Solutions

Expert Solution

Solution:
a. Firm make a profit on this asset $ 57,606.08
Working Notes:
Firm make a profit on this asset
= Present value of sale value of 7th year today - cost today to produce
= (Sale value/(1+required rate of return)^n ) - cost today to produce
= (220000/(1+ 0.075)^7 ) - 75,000
= 132606.0782- 75,000
=$57,606.08
Now calculate this using Excel method
=PV(rate,nper,pmt, fv)
Here
PV= Present value of sale value of assets today =??
rate = 7.5%
nper= n = 7 years
pmt= 0 = any periodic cash flows
FV= sale value at end of 7 th year = $220000
=PV(rate,nper,pmt, fv)
=PV(7.5%,7,0, 220000)
($132,606.08) negative sign shows today present value outflows for payment of cash inflows in 7 th year of 220,000
Profit = Present value today -today cost to produce
Profit = 132,606.08 -75,000
Profit = $57,606.08
b. Rate for the firm just break even 16.62 %
Working Notes:
Rate for the firm just break even
to break even means profit is zero
present value 7th year sale value today is today cost to produce
let r be Rate for the firm just break even
Firm make a profit on this asset = 0
0= Present value of sale value of 7th year today - cost today to produce
0= (Sale value/(1+required rate of return)^n ) - cost today to produce
0= (220000/(1+ r )^7 ) - 75,000
75,000 =    220000/(1+ r )^7
(1+ r )^7 = 220,000/75,000
r = (220,000/75,000)^(1/7) - 1
r = 0.16618088
r = 16.62%
Now by excel method
=RATE(nper,pmt,pv,fv)
Here  
PV= Present value of sale value of assets today =-75000 cost to produce
rate = ??
nper= n = 7 years
pmt= 0 = any periodic cash flows
FV= sale value at end of 7 th year = $220000
=RATE(nper,pmt,pv,fv)
=RATE(7,0,-75000,220000)
16.62%
Please feel free to ask if anything about above solution in comment section of the question.

jeff jeffy answered 1 year ago
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