Homework Clinic
Social Science Clinic => Economics => Topic started by: xsk4r3kr0w on Nov 23, 2022
-
Question 1
Financial Markets
You are considering buying a machine that costs $1,211.79. If purchased, the machine yields the income stream shown in the table for the next 7 years.
| Year | Income |
| 1 | 485 |
| 2 | 275 |
| 3 | 390 |
| 4 | 330 |
| 5 | 0 |
| 6 | 0 |
| 7 | 0 |
Would you buy the machine if the interest rate was 8%? 10%?
◦ no, no
◦ no, yes
◦ yes, no
◦ yes, yes
Question 2
Capital Accumulation
Suppose you lend 10,000 to a friend for a year. In that year, the real rate of return in the stock market is 4%. What is the minimum amount your friend needs to pay you back to make the loan worthwhile?
Please round your final answer to two decimals.
◦ $10,400.00
◦ $20,000
◦ $9,600.00
◦ $10,000
-
Answer 1
yes, no
To determine whether you would buy the machine, you need to compare the present value of the income stream for the machine (PV) to the costs.
If the cost is greater than the present value of the income stream, then you should not buy the machine.
If the cost is less than or equal to the present value of the income stream, then you should buy the machine.
At 8%:
PV = Income1/(1+i) + Income2/(1+i)^2 + Income3/(1+i)^3 + Income4/(1+i)^4 + Income5/(1+i)^5 + Income6/(1+i)^6 + Income7/(1+i)^7
PV = 485/(1.08) + 275/(1.08)^2 + 390/(1.08)^3 + 330/(1.08)^4
PV = 449.07 + 235.768176 + 309.594574 + 261.96464 = $1,237.00
Because 1,237.00 is greater than 1,211.79, you should buy the machine.
At 10%:
PV = Income1/(1+i) + Income2/(1+i)^2 + Income3/(1+i)^3 + Income4/(1+i)^4 + Income5/(1+i)^5 + Income6/(1+i)^6 + Income7/(1+i)^7
PV = 485/(1.10) + 275/(1.10)^2 + 390/(1.10)^3 + 330/(1.10)^4
PV = 440.91 + 227.27 + 293.01 + 225.39 = $1,186.58903
Because 1,186.58903 is less than 1,211.79, you should not buy the machine.
Answer 2
$10,400.00
You need to compute the opportunity cost of lending money to your friend. If you had not lent the money, you could have invested it in the stock market where you would have earned 4% per year.
Therefore, the present value (PV) of the amount your friend must pay you back, discounted at 4%, must be equal to the $10,000 you lent.
PV = Payback Amount/(1+i)
10,000 = Payback Amount/(1+ (4/100))
Payback Amount = 10,000*(1+ (4/100)) = 10,000*1.04 = $10,400.00