Answer:
1(a) PV for Sally if she goes to school = $38,322.00
1(b) PV for Sally if she does not go to school = $37,188.21
1(c) Since the present value for Sally if she goes to school of $38,322.00 is greater than the present value if she does of $37,188.21, the investment in school makes sense.
2(a) PV for Sally if she goes to school = $37,557.85
2(b) PV for Sally if she does not go to school = $36,667.85
2(c) Since the present value for Sally if she goes to school of $37,557.85 is greater than the present value if she does not of $36,667.85, the investment in school makes sense.
3(a) PV for Sally if she goes to school = $39,108.73
3(b) PV for Sally if she does not go to school = $36,667.85
3(c) Since the present value for Sally if she goes to school of $39,108.73 is greater than the present value if she does not of $37,721.89, the investment in school makes sense.
Explanation:
Note: This question is not complete. The complete question is provided before answering the question as follows:
Sally has a decision to make about what she will do in the next 2 years. She can go to school or go straight into the workforce. If Sally immediately starts working, she will earn $20,000 in both years 1 and 2. If she goes to school in year 1, she must pay $5,000, but she would earn $47,500 in year 2. If the interest rate is 5%, calculate the present value for Sally if she goes to school and if she does not. Does the investment in school make sense? Does it make sense if the interest rate is 6% or 4%?
The explanation of the answer is now provided in 3 parts as follows:
To calculate the present value of an amount, the following formula is used:
PV = FV / (1 + r)^n ………………. (1)
Where:
PV = present value of an amount
FV = Future value an amount in a particular year
r = interest rate
n = the year in focus
Therefore, we have:
1(a) If the interest rate is 5%, calculate the present value for Sally if she goes to school
Using equation (1), we have:
PV of amount to pay in Year 1 = $5,000 / (1 + 0.05)^1 = $4,761.90
PV of earnings in Year 2 = $47,500 / (1 + 0.05)^2 = $43,083.90
Present value for Sally if she goes to school = PV of earnings in Year 2 earnings - PV of amount to pay in Year 1 = $43,083.90 - $4,761.90 = $38,322.00
1(b) If the interest rate is 5%, calculate the present value for Sally if she does not go to school
Using equation (1), we have:
PV of Year 1 earnings = $20,000 / (1 + 0.05)^1 = $19,047.62
PV of Year 2 earnings = $20,000 / (1 + 0.05)^2 = $18,140.59
Present value for Sally if she does not go to school = PV of Year 1 earnings + PV of Year 2 earnings = $19,047.62 + $18,140.59 = $37,188.21
1(c.) Does the investment in school make sense?
From parts 1(a) and 1(b) above, since the present value for Sally if she goes to school of $38,322.00 is greater than the present value for Sally if she does not go to school of $37,188.21, the investment in school makes sense.
2(a) If the interest rate is 6%, calculate the present value for Sally if she goes to school
Using equation (1), we have:
PV of amount to pay in Year 1 = $5,000 / (1 + 0.06)^1 = $4,716.98
PV of earnings in Year 2 = $47,500 / (1 + 0.06)^2 = $42,274.83
Present value for Sally if she goes to school = PV of earnings in Year 2 earnings - PV of amount to pay in Year 1 = $42,274.83 - $4,716.98 = $37,557.85
2(b) If the interest rate is 6%, calculate the present value for Sally if she does not go to school
Using equation (1), we have:
PV of Year 1 earnings = $20,000 / (1 + 0.06)^1 = $18,867.92
PV of Year 2 earnings = $20,000 / (1 + 0.06)^2 = $17,799.93
Present value for Sally if she does not go to school = PV of Year 1 earnings + PV of Year 2 earnings = $18,867.92 + $17,799.93 = $36,667.85
2(c.) Does the investment in school make sense?
From parts 2(a) and 2(b) above, since the present value for Sally if she goes to school of $37,557.85 is greater than the present value for Sally if she does not go to school of $36,667.85, the investment in school makes sense.
3(a) If the interest rate is 4%, calculate the present value for Sally if she goes to school
Using equation (1), we have:
PV of amount to pay in Year 1 = $5,000 / (1 + 0.04)^1 = $4,807.69
PV of earnings in Year 2 = $47,500 / (1 + 0.4)^2 = $43,916.42
Present value for Sally if she goes to school = PV of earnings in Year 2 earnings - PV of amount to pay in Year 1 = $43,916.42 - $4,807.69 = $39,108.73
3(b) If the interest rate is 6%, calculate the present value for Sally if she does not go to school
Using equation (1), we have:
PV of Year 1 earnings = $20,000 / (1 + 0.04)^1 = $19,230.77
PV of Year 2 earnings = $20,000 / (1 + 0.04)^2 = $18,491.12
Present value for Sally if she does not go to school = PV of Year 1 earnings + PV of Year 2 earnings = $19,230.77 + $18,491.12 = $37,721.89
3(c.) Does the investment in school make sense?
From parts 3(a) and 3(b) above, since the present value for Sally if she goes to school of $39,108.73 is greater than the present value for Sally if she does not go to school of $37,721.89, the investment in school makes sense.
