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. | |||
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