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 | |||||||