Replacement of equipment. I own an old car that is worth about $3,000. As long as I keep fixing it, that salvage value is constant. It costs $5,000/year to maintain and fuel the car. Elon Musk tweeted this regarding the Tesla 3.

https://twitter.com/elonmusk/status/639171519197777920

Suppose we are considering buying the Tesla 3 now

(Solve the questions form the attachment)

FNCE 451/751 Assignment 2 Due Feb 22/23 Beware reading week 1. Replacement of equipment. I own an old car that is worth about $3,000. As long as I keep fixing it, that salvage value is constant. It costs $5,000/year to maintain and fuel the car. Elon Musk tweeted this regarding the Tesla 3. https://twitter.com/elonmusk/status/639171519197777920 Suppose we are considering buying the Tesla 3 now The Tesla 3 will cost $35,000, but has much lower fuel and maintenance costs of only $500/year. All these figures are real dollars. Suppose the resale value of the Tesla after 7 years is $10,000. Use a 10% real discount rate. Spreadsheet: a. What is the 7-year present value of costs for my old car? (include final salvage) b. What is the 7-year present value of costs for the Tesla 3 replacement? (include initial salvage and final resale) c. On a 7-year horizon, what is the annual lease equivalent for each car? In other words, convert the cash flows to a 7-year annuity. On a spreadsheet you can use guess-andcheck (or goal seek, or PMT function); on paper use the A(7,10%)=4.868 annuity factor. Try all of these methods. d. Perhaps the $10,000 terminal value is wrong. We could estimate is that value based on the economics of the gas savings. Since the Tesla generates $4,500/year of operating savings versus the old car (not including initial price), we could estimate a terminal valuation using a \"multiple\" of annual savings. Use a 4X multiple, plus the old-car base salvage (any drivable car has a base utility), to re-estimate the constant resale. What is the 7-year annual lease equivalent now? 2. Efficient Frontier for a Canadian balanced portfolio. a. I will give monthly return data for TSX and FTSE bond index from 1982. Contract a total return series for each that starts at 1 (monthly compounding). Consider also a monthly rebalanced balanced portfolio, say 60%/40%, and let the mix be a parameter you can control. Chart the total returns for all 3 columns. SUMPRODUCT() is a good way to apply the mix. b. Compute the annualized arithmetic mean return and standard deviation of returns (multiply by 12 and square root of 12) for each class and the blend. Compute the geometric mean also and the correlation between bonds and equities. Using a 3-year moving window you can check how the correlation has varied over time. c. Make an assumption about forward-looking returns for each asset class. For bonds the current yield is a very good estimate (even better than you think) http://www.cfapubs.org/doi/sum/10.2469/faj.v70.n1.5. For equities we normally use an equity risk premium approach. For example ERP=10% and many alternatives in this recent paper. http://www.newyorkfed.org/research/staff_reports/sr714.pdf d. We will have to use the historical data to estimate forward-looking volatility and correlations. Now you can consider the whole range of bond/equity asset mixes. From 100% bonds to 50/50 to 100% equity. For each mix (say jumps of 10%) compute the standard deviation and return, based on the forward looking returns. Note that the returns are just a linear combination of expected returns, but volatility is not linear because of the correlations. Use these risk/return pars to make an efficient frontier dot plot (standard deviation versus expected return). e. You should notice that starting from all bonds we move very slightly to the left (lower risk) as we add a little equity to the portfolio. That equity also obviously increases the return too. f. Another way to characterize risk is to look at a \"2008 stress test\". Invent a stress test based on that market event (using the actual returns) and apply it to the sample balanced portfolios. 3. Efficient Frontier for a Canadian balanced portfolio with hedged USD High Yield Bonds included Use the High Yield historical performance data to optimize 3-asset portfolios of equity, bonds, and HY bonds. Since there are more than 2 assets, the risk/return possibilities span an area. Find portfolios on the efficient frontier. Find also the ERC (equal risk contribution) portfolio, give its risk/return, and plot on a risk/return chart. You need to run the solver here to optimize return for each risk