Tutor profile: Oscar N.
Subject: Personal Finance
John wishes to buy a brand-new $40,000 Tesla Model 3. He will use $10,000 that he has saved as a down-payment and will borrow the rest. He requested a loan at a bank and was offered a 5-year fixed 10% APR loan with monthly payments. How much are the monthly payments?
We are given that John is borrowing $30,000 from the bank at a 10% APR for 5 years. With a financial calculator, we could solve for the monthly payment with the following inputs: N = 5 years * 12 payment per year = 60 I/Y = 10% APR/12 months per years = 1% PV = $30,000 PMT = ? FV = $0 Computing for the PMT, we get that the monthly payments will be $667.33. Alternatively, we could use the annuity PV formula to determine the monthly payment: PV of annuity = PMT*1/r*(1-1/(1+r)^t) = PMT*Annuity Factor PMT of annuity = PV/Annuity factor PV is the present value, r is the periodic interest rate (annual interest rate/# of compounding periods per year), t is the number of periods (# of years * # periods per year) In this case, PV = $30,000, r = 12%/12 monthly payment = 1%, t = 5 years * 12 payment per year = 60. Annuity factor = 1/1%*(1-1/(1+1%)^60) = 44.95503841 PMT = $30,000/44.95503841 = $667.33
Subject: Corporate Finance
TutorMe's stock is expected to pay a $5 dividend in 1 year and its dividends are expected to grow at 5% per year in perpetuity. If TutorMe's cost of capital is 10%, what's the company's current stock price according to the Gordon growth model?
The Gordon growth model states that if the dividends of a company are expected to grow at a constant rate forever, then the following formula can be used to find its current price: Current price = Expected dividend next year/(Cost of capital - dividend growth rate). In this case: Expected dividend = $5 Cost of capital = 10% Dividend growth rate = 5% Current price = $5/(10%-5%) = $100 Therefore, TutorMe's current stock price is $100.
You are given the following two options: $100,000 right now or $150,000 in 2 years. Both options are certain, meaning that the probability that you will receive your selected option is 100%. Assuming you could invest your money at an effective 8% return per year, which of the two options is better?
To determine which option is better, we need to make an apple to apple comparison of the value of the two sums. For that, we can calculate the present value (or future value) of each option and compare it against that of the other option. The present value of $100,000 today is simply that since it happens today. The present value of $150,000 in 2 years can be calculated using the present value formula: PV = FV/(1+r)^t, where PV is the present value, FV is the future value, r is the discount rate (rate of return), and t is the number of years until the cash flow is received. In the case of the second option: PV = $150,000/(1+8%)^2 = $128,600.82. The second option has a higher present value, therefore it is better.
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