In: Accounting
2.Find the future value in 7 years of the following cash flows: 2,000 in 2 years and 7,000 in 4 years. The interest rate is 7.6% p.a. compounded monthly for the first 5 years and 5.8% p.a. compounded half-yearly thereafter. (Correct your answer to the nearest cent without any unit (No need to put "$"). Do not use "," in your answer. e.g. 123456.78))
3.Your uncle offers to sell you his vintage Rolls Royce. He suggests a payment plan where you pay just $17,000 today, $7000 in 11 months and $12,000 in exactly 20 months from today. If the interest rate is 5.4% per annum compounding monthly, what is the value of the offer (in present day dollars, rounded to the nearest dollar; don’t show $ sign or commas)?
| Future Value of Cash Flow =(Cash Flow)*((1+i)^N) | |||||||
| i=Interest Rate | |||||||
| N=Number of years to the future | |||||||
| Interest Rate for first 5 years: | |||||||
| 7.6% compounded monthly | |||||||
| Monthly interest rate =(7.6/12)% | 0.6333% | 0.006333 | |||||
| Effective annual interest rate =R | |||||||
| 1+R=(1+0.006333)^12= | 1.0787 | ||||||
| Effective annual interest rate =R= | 0.0787 | 7.87% | |||||
| Future Value of Cash Flow in 5 years | |||||||
| t | N=(5-t) | CF | FV5=CF*(1.0787^N) | ||||
| Year | Number of years to future | Cash Flow | Future value at end of year 5 | ||||
| 2 | 3 | $2,000 | $2,510.37 | ||||
| 4 | 1 | $7,000 | $7,550.93 | ||||
| Total | $10,061.29 | ||||||
| Interest Rate after 5 years: | |||||||
| 5.8% compounded halfyearly | |||||||
| Half yearly interest rate =(5.8/2)% | 2.90% | 0.0290 | |||||
| Effective annual interest rate =R | |||||||
| 1+R=(1+0.0290)^2= | 1.058841 | ||||||
| Effective annual interest rate =R= | 0.058841 | 5.8841% | |||||
| N= | Number of years to future =7-5 | 2 | |||||
| i= | Annual effective interest rate | 0.058841 | |||||
| Future value at end of Year 7 | $11,280.16 | (1061.29*(1.058841^2) | |||||
| ANSWER: | |||||||
| 11280.16 | |||||||
| 3 | Present Value of Cash Flow =(Cash Flow)/((1+i)^N) | ||||||
| i=Interest Rate per month=(5.4/12)% | 0.45% | 0.0045 | |||||
| N=Month of Cash Flow | |||||||
| N | CF | PV=CF/(1.0045^N) | |||||
| Month | Cash Flow | Present Value | |||||
| 0 | $17,000 | $17,000.00 | |||||
| 11 | $7,000 | $6,662.68 | |||||
| 20 | $12,000 | $10,969.39 | |||||
| SUM | $34,632.06 | ||||||
| Value of the offer | $34,632.06 | ||||||
| ANSWER: | |||||||
| 34,632 | |||||||