10 - Assignment 3 - CT PDF

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Finance 1

Feb 22, 2021 FIN603 N1A

Assignment 3

1. You are planning to retire in 15 years, you’ve determined that you can afford to save $500 per week. How much will you have saved at the end of the 15 years, if you can earn 6% compounded quarterly? 10 marks Since the compounding is quarterly, we’ll state our investment annuity all in quarterly terms for ease of calculation: n = 15 years x 4 quarter / year = 60 quarters i = 6%/4 = 1.5% PMT = $500/week x 13 weeks / quarter = $6,500.00 / quarter This may be disputed but we’ll assume a 13 week quarter, though a quarter is not always exactly 13 weeks. Now we can either use the formula:

FV =PMT 6,500

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( 1+i )n−1 i

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=

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60 ( 1+ 0.015) −1 2.44322−1 2.44322−1 =6,500 =6,500 =6,500 × 96.21465=625,395.24 0.015 0.015 0.015

/ANS. Alternatively we can use excel to with the PV formula =FV(1.5% ,60,-6500,0,0) = $625,395.24 2. You are planning to retire in 35 years, you’ve determined that you can afford to save $200 per week. How much will you have saved at the end of the 35 years, if you can earn 5.7% compounded Monthly? 10 Marks Since the compounding is monthly, we’ll state all our values on a monthly basis: n = 35 years x 12 months/year = 420 months i= 5.7% /12 = 0.475% per month PMT = $200 / week x 4.34524 weeks / month = 869.048 / month to be more exact we used the average 4.34524 weeks per month. Now we can either use the formula:

FV =PMT

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[

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n 420 ( 1+i ) −1 ( 1+0.00475 ) −1 7.317559−1 =869.048 =869.048 =869.048 ×1,330.012 i 0.00475 0.00475

/Ans Or, we can use the Excel FV formula: =FV(0.475%,420,-869.048,0,0) = $1,155,844.67 3. Someone has offered you $50 per week for the rest of your life, if the discount rate is 10%, how much would you be willing to pay for this cashflow? 20 Marks Assuming $50 per week in a year we should have 52.1429 weeks/year x $50 / week = $2,607.15 per year in cash flow annually. Assuming this is a perpetuity, the present value would be:

PV =

PMT $ 2,607.15 =$ 26,071.45 /ANS = 10 % i

This means that we should be willing to pay 26,071.45 for this perpetuity/cashflow.

4. You want to buy a house in Scarborough for $563,000. You plan to make a down

Finance 1

Assignment 3

Feb 22, 2021 FIN603 N1A

payment of $73,190 and you intend to borrow the remainder with a mortgage. The bank offers you a 5 year term and quotes a rate of 5.95% compounded semannually, amortized over a 25 year period. You elect to make semi-monthly (bimonthly payments ie-2 payments per month). How much will you owe at the end of the 5 year period? 20 Marks The house costs: 563,000, but the down payment is 73,190 which means that the amount borrowed is: House Cost Down Pmt Amt Borrowed

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563,000 73,190 489,810

Now the compounding is semi-annually (every semester) so we’ll state all our values on this framework: n1 (amortization term) = 25 years x 2 semesters/year = 50 semesters n2 (repayment term) = 5 years x 2 semesters/year = 10 semesters i = 5.95 % / 2 = 0.02975 First we’ll need to solve for the payments on the amortization term: For ease, we’ll use the excel formula: =PMT(0.02975,50,489810,0,0) Which gives us -$18,946.44 as the cashflows per semester and we know that 2 payments per month are being made or 12 payments in a semester, however, for our purposes, we’ll ignore the semi-monthly payment since our compounding term is semi-annually. Then we’ll solve for the future value (FV) of the payments at the 5 year point (i.e. n2 – repayment term of 10 semesters). To do so, we’ll use the FV formula in excel: =FV(0.02975,10,18946.44,-489810,0) which gives us $439,717.90 as the amount owing or residual at the end of the 5 year period. /ANS 5. You’ve won the lottery, a $1000 per week cash payment for 25 years, then a lump sum payment of $1,000,000. If the interest rate is 8%, how much will you be willing to accept today instead? 20 Marks We have two cashflows a future value lump sum and an annuity. We’ll treat them separately (particularly if using the formulas) for present value purposes then add their combined PVs to establish the answer. First, the lump sum: FV = 1,000,000 n = 25 years i = 8% / year so with excel: =PV(0.08,25,0,-1000000,0) which gives us: 146,018 as the PV of the lump sum next, the annuity: n = 25 years i = 8% / year PMT = $1000 / week x 52.1429 weeks / year = 52,143 / year on average

Finance 1

Assignment 3

Feb 22, 2021 FIN603 N1A

So with excel: =PV(0.08,25,-52143,0,0) Which gives us: 556,615 as the PV of the annuity So the PV combined is 146,018 + 556,615 = 702,633 which would be the lumpsum we should accept today. /ANS...