Question

Your friends and you decide to purchase a large tract of forest land in northern Minnesota with the intent of generating income from timber and leasing the hunting rights. Your estimated costs and returns are as follows:

• $1400/acre purchase price of land, paid back in equal yearly installments over 15 years @ 7% annual interest.

• $200/acre site preparation costs incurred immediately.

• $250/acre tree planting costs incurred 1 year after purchase.

• $100/acre forest management costs incurred 3, 4, 5, 6, and 7 years after purchase.

• $50/acre forest management costs incurred 8, 9, and 10 years after purchase.

• Annual hunting lease of $75/acre beginning in years 2 years after purchase and continuing until 15 years after purchase.

• $7/acre annual property taxes, beginning immediately and paid each year you own the land through 15 years after purchase.

• $4,500/acre income from the sale of timber 13 years after purchase.

• $1,200/acre from the sale of your forest land 16 years after purchase.

• Your discount rate is 5.5%.

1-What amount will you have to pay each year for the loan payment associated with purchasing the land?

2-What is the present value of all loan payments?

3-What is the present value of the last loan payment associated with purchasing the forest land?

4-What is the present value of the site preparation costs?

5- What is the present value of the tree planting costs?

6-What is the present value of the $100/acre forest management costs (all years)?

7-What is the present value of the last $50/acre forest management cost?

8-What is the present value of the last $50/acre forest management cost?

9-What is the present value of the last lease payment?

10-What is the present value of all hunting lease revenue?

11-What is the present value of the revenue generated from the timber sale?

12-What is the present value of the revenue generated from the sale of your forest land?

13-What is the present value of the property taxes (all years)?

14-What is the present value of all costs incurred in year 10?

15-What is the present value of all revenue generated in year 2?

16-What is the net present value of all costs incurred and revenue generated in year 6?

Answer 1

1)EMI = [P x R x (1+R)^N]/[(1+R)^N-1]
, where P stands for the loan amount or principal, R is the interest rate per month, and N is the number of monthly instalments.
P=1400
R=7%
N=15
EMI=(1400*7%*(1+7%)^15)/((1+7%)^15-1)
=153.71

2)PV of all loan repayment is 1542.88.

Y1	153.71	=+153.71/1.055	145.70
Y2	153.71	=+153.71/(1.055)^2	138.10
Y3	153.71	=+153.71/(1.055)^3	130.90
Y4	153.71	=+153.71/(1.055)^4	124.08
Y5	153.71	=+153.71/(1.055)^5	117.61
Y6	153.71	=+153.71/(1.055)^6	111.48
Y7	153.71	=+153.71/(1.055)^7	105.67
Y8	153.71	=+153.71/(1.055)^8	100.16
Y9	153.71	=+153.71/(1.055)^9	94.94
Y10	153.71	=+153.71/(1.055)^10	89.99
Y11	153.71	=+153.71/(1.055)^11	85.30
Y12	153.71	=+153.71/(1.055)^12	80.85
Y13	153.71	=+153.71/(1.055)^13	76.63
Y14	153.71	=+153.71/(1.055)^14	72.64
Y15	153.71	=+153.71/(1.055)^15	68.85
Total	2305.65		1,542.88

3) PV of Last Loan repayment=

153.71

=+153.71/(1.055)^15

= 68.85

4) PV of site preparation cost=200

5) PV of Tree planting cost :

250

250/(1.055)^2

224.61

6) present value of the $100/acre forest management costs (all years)=383.65

Y3	100	85.16
Y4	100	80.72
Y5	100	76.51
Y6	100	72.52
Y7	100	68.74
		383.65

7)present value of the last $50/acre forest management cost?=29.27

Y10

50

=50/(1.055)^10

29.27

8)

present value of the last $50/acre forest management cost?=29.27

Y10

50

=50/(1.055)^10

29.27

9) present value of the last lease payment=33.59

Y15

75

=75/(1.055)^15

33.59

10)present value of all hunting lease revenue:681.72

Year Amount PV of Y1 0 Y2 75 75/(1.055)^2 67.38 Y3 75 75/(1.055)^3 63.87 Y4 75 75/(1.055)^4 60.54 Y5 75 75/(1.055)^5 57.39 Y6 75 75/(1.055)^6 54.39 Y7 75 75/(1.055)^7 51.56 Y8 75 75/(1.055)^8 48.87 Y9 75 75/(1.055)^9 46.32 Y10 75 75/(1.055)^10 43.91 Y11 75 75/(1.055)^11 41.62 Y12 75 75/(1.055)^12 39.45 Y13 75 75/(1.055)^13 37.39 Y14 75 75/(1.055)^14 35.44 Y15 75 75/(1.055)^15 33.59 Total 681.72

11)present value of the revenue generated from the timber sale=2243.52

Y13 =4500

=4500/(1.055)^13

=2243.52

12) present value of the revenue generated from the sale of your forest land=509.5

Y16=1200=1200/(1.055)^16=509.50

13)present value of the property taxes (all years)=63.63

Year	Amount		PV of
Y1	7	7	7
Y2	7	7/(1.055)^2	6.29
Y3	7	7/(1.055)^3	5.96
Y4	7	7/(1.055)^4	5.65
Y5	7	7/(1.055)^5	5.36
Y6	7	7/(1.055)^6	5.08
Y7	7	7/(1.055)^7	4.81
Y8	7	7/(1.055)^8	4.56
Y9	7	7/(1.055)^9	4.32
Y10	7	7/(1.055)^10	4.1
Y11	7	7/(1.055)^11	3.88
Y12	7	7/(1.055)^12	3.68
Y13	7	7/(1.055)^13	3.49
Y14	7	7/(1.055)^14	3.31
Y15	7	7/(1.055)^15	3.14
Total			63.63

14) present value of all costs incurred in year 10

=Land procurement+Site preparation+tree planting+forest management costs+annual property tax
=89.99+0+0+29.27+4.1

=123.36

15)present value of all revenue generated in year 2=67.38

Lease =75=75/(1.055)^2=67.38

16)net present value of all costs incurred and revenue generated in year 6

=Land procurement+Site preparation+tree planting+forest management costs+annual property tax-Lease

=111.48+0+0+72.52+5.08-54.39

=134.69