Financial Management: Annuity, EMI, and Incremental Analysis
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This article covers topics such as future value of annuity, present value of annuity, EMI calculation, sunk cost, incremental analysis, and more related to financial management.
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Question 2 (a) (i)Future value of annuity Now, It is apparent that Ruth has to achieve the target of $1,600,000 at the age of 63. However, he would not be able to achieve it as apparent from future value of annuity(Arnold, 2015). (ii)Present value of annuity would be used to find the monthly pension (Parrino and Kidwell, 2014). 1
Now, P = $9,351.52 Thus, at the end of each month Ruth will get a monthly pension of9,351.52 after a month of retirement. (b) (i)Compounding = Monthly Nominal interest rate = 4.5% p.a. (ii)Calculation of EMI (equal monthly instalment ) (Damodaran, 2015). Now, (iii)Sum of present value of annuities would be equal to the loan amount ($750,000) (Damodaran, 2015). 2
PV of annuity of $ 3000 per month (first 12 months) = 3000*(1-1.00375-12)/0.00375 = $ 35,137.64 PV of annuity of $ 3,500 per month (paid during 2nd year) = [3500*(1-1.00375-12)/0.00375] /1.0037512= $ 39.193.38 PV of annuity of $ Y per month (paid during remaining 23 years) = [Y*(1-1.00375-(23*12)) /0.00375] /1.0037524= 157Y Now, (iv)Present value of annuity(Arnold, 2015) R = 4.5% p.a. or (4.5/12) = 0.375% per month P = $4,400 PV of annuity = $750,000 N =? 3
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The end payment would be lower than the $4,400. Question 4 (a) The amount paid to the consultants i.e. $ 25,000 would be a sunk cost since it cannot be recovered and hence it would not be taken in consideration. Only, incremental and recoverable costs and benefits are considered (Damodaran, 2015). Information for hydrofoils Initial cost for the two hydrofoils at t=0 is (480000*2) or $ 960,000 Salvage value at the end of four years = 75000 8 2 = $ 150,000 Annual depreciation based on straight line method = (960000-150000)/4 = $202,500 Information for existing ferries Current sale price = 170000*3 = $ 510,000 Cost price (two years ago) = 300000*3 = $ 900,000 Annual depreciation = 900000/6 = $ 150,000 Current book value of three ferries = 900000 – (2*150000) = $ 600,000 Company would bear loss on sale of ferries to the extent of (600000-510000) or $ 90,000 on which tax benefit of 0.3*90000 or $ 27,000 would be realised (Northington, 2015). Incremental Analysis Initial investment = Cost of hydrofoils – Sale of ferries + working capital = 960,000- 510,000 + 30,000 = $ 480,000 The working capital $ 30,000 would be recovered at end of year 4 Incremental annual depreciation = Annual depreciation on hydrofoils – Annual depreciation on existing ferries = 202500 – 150000 = $52,500 4
The computation of NPV is shown below. Thus, the NPV of the project is $ 21,716. (b) The company should replace the existing ferries with hydrofoils since the NPV of the project is positive and hence it would generate wealth for the shareholders (Arnold, 2015). 5
References Arnold,G.(2015)CorporateFinancialManagement.3rded.Sydney:FinancialTimes Management. Damodaran, A. (2015).Applied corporate finance: A user’s manual3rd ed. New York: Wiley, John & Sons. Northington, S. (2015)Finance, 4thed. New York: Ferguson Parrino, R. and Kidwell, D. (2014)Fundamentals of Corporate Finance,3rd ed. London: Wiley Publications . 6