Question

Highland Mining and Minerals Co. is considering the purchase of two gold mines. Only one investment will be made. The Australian gold mine will cost $1,671,000 and will produce $381,000 per year in years 5 through 15 and $592,000 per year in years 16 through 25. The U.S. gold mine will cost $2,041,000 and will produce $267,000 per year for the next 25 years. The cost of capital is 8 percent. Use Appendix D for an approximate answer but calculate your final answers using the formula and financial calculator methods. (Note: In looking up present value factors for this problem, you need to work with the concept of a deferred annuity for the Australian mine. The returns in years 5 through 15 actually represent 11 years; the returns in years 16 through 25 represent 10 years.)
  
a-1. Calculate the net present value for each project. (Do not round intermediate calculations and round your answers to 2 decimal places.)
  

   
a-2. Which investment should be made?
  

• Australian mine

• U.S. mine

  
b-1. Assume the Australian mine justifies an extra 3 percent premium over the normal cost of capital because of its riskiness and relative uncertainty of cash flows. Calculate the new net present value given this assumption. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.)
  

  
b-2. Does the new assumption change the investment decision?
  

• yes

• No

Answer 1

Point a-1

Cash Flow table for Australian Gold Mine

Year	Cash Flow	PV Factor	Calculation	Present Value
0	-1671000	1	1/(1+0.08)^0	-1671000
1	0	0.93	1/(1+0.08)^1	0
2	0	0.86	1/(1+0.08)^2	0
3	0	0.79	1/(1+0.08)^3	0
4	0	0.74	1/(1+0.08)^4	0
5	381000	0.68	1/(1+0.08)^5	259302.20
6	381000	0.63	1/(1+0.08)^6	240094.63
7	381000	0.58	1/(1+0.08)^7	222309.84
8	381000	0.54	1/(1+0.08)^8	205842.44
9	381000	0.50	1/(1+0.08)^9	190594.86
10	381000	0.46	1/(1+0.08)^10	176476.72
11	381000	0.43	1/(1+0.08)^11	163404.37
12	381000	0.40	1/(1+0.08)^12	151300.34
13	381000	0.37	1/(1+0.08)^13	140092.91
14	381000	0.34	1/(1+0.08)^14	129715.66
15	381000	0.32	1/(1+0.08)^15	120107.09
16	592000	0.29	1/(1+0.08)^16	172799.16
17	592000	0.27	1/(1+0.08)^17	159999.22
18	592000	0.25	1/(1+0.08)^18	148147.43
19	592000	0.23	1/(1+0.08)^19	137173.54
20	592000	0.21	1/(1+0.08)^20	127012.54
21	592000	0.20	1/(1+0.08)^21	117604.20
22	592000	0.18	1/(1+0.08)^22	108892.78
23	592000	0.17	1/(1+0.08)^23	100826.65
24	592000	0.16	1/(1+0.08)^24	93358.01
25	592000	0.15	1/(1+0.08)^25	86442.60

NPV = sum of the present value column = $ 1,580,497.17

Cash Flow table for US Gold Mine

Year	Cash Flow	PV Factor	Calculation	Present Value
0	-2041000	1	1/(1+0.08)^0	-2041000
1	267000	0.93	1/(1+0.08)^1	247222
2	267000	0.86	1/(1+0.08)^2	228909
3	267000	0.79	1/(1+0.08)^3	211953
4	267000	0.74	1/(1+0.08)^4	196253
5	267000	0.68	1/(1+0.08)^5	181715.71
6	267000	0.63	1/(1+0.08)^6	168255.29
7	267000	0.58	1/(1+0.08)^7	155791.94
8	267000	0.54	1/(1+0.08)^8	144251.79
9	267000	0.50	1/(1+0.08)^9	133566.47
10	267000	0.46	1/(1+0.08)^10	123672.66
11	267000	0.43	1/(1+0.08)^11	114511.72
12	267000	0.40	1/(1+0.08)^12	106029.37
13	267000	0.37	1/(1+0.08)^13	98175.35
14	267000	0.34	1/(1+0.08)^14	90903.10
15	267000	0.32	1/(1+0.08)^15	84169.54
16	267000	0.29	1/(1+0.08)^16	77934.75
17	267000	0.27	1/(1+0.08)^17	72161.81
18	267000	0.25	1/(1+0.08)^18	66816.49
19	267000	0.23	1/(1+0.08)^19	61867.12
20	267000	0.21	1/(1+0.08)^20	57284.37
21	267000	0.20	1/(1+0.08)^21	53041.08
22	267000	0.18	1/(1+0.08)^22	49112.12
23	267000	0.17	1/(1+0.08)^23	45474.18
24	267000	0.16	1/(1+0.08)^24	42105.72
25	267000	0.15	1/(1+0.08)^25	38986.78

NPV = sum of the present value column = $ 809,165.24

Point a-2

Austrailian Gold mine should be selected as it has a higher NPV

Point b-1

New Cost of Capital for Austrailian Gold Mine = 8+3 = 11%

Cash Flow table under new circumstances is depicted below:

Year	Cash Flow	PV Factor	Calculation	Present Value
0	-1671000	1	1/(1+0.11)^0	-1671000
1	0	0.90	1/(1+0.11)^1	0
2	0	0.81	1/(1+0.11)^2	0
3	0	0.73	1/(1+0.11)^3	0
4	0	0.66	1/(1+0.11)^4	0
5	381000	0.59	1/(1+0.11)^5	226104.96
6	381000	0.53	1/(1+0.11)^6	203698.16
7	381000	0.48	1/(1+0.11)^7	183511.85
8	381000	0.43	1/(1+0.11)^8	165326.00
9	381000	0.39	1/(1+0.11)^9	148942.34
10	381000	0.35	1/(1+0.11)^10	134182.29
11	381000	0.32	1/(1+0.11)^11	120884.94
12	381000	0.29	1/(1+0.11)^12	108905.35
13	381000	0.26	1/(1+0.11)^13	98112.93
14	381000	0.23	1/(1+0.11)^14	88390.03
15	381000	0.21	1/(1+0.11)^15	79630.66
16	592000	0.19	1/(1+0.11)^16	111468.98
17	592000	0.17	1/(1+0.11)^17	100422.51
18	592000	0.15	1/(1+0.11)^18	90470.73
19	592000	0.14	1/(1+0.11)^19	81505.16
20	592000	0.12	1/(1+0.11)^20	73428.07
21	592000	0.11	1/(1+0.11)^21	66151.42
22	592000	0.10	1/(1+0.11)^22	59595.87
23	592000	0.09	1/(1+0.11)^23	53689.97
24	592000	0.08	1/(1+0.11)^24	48369.35
25	592000	0.07	1/(1+0.11)^25	43575.99

NPV = sum of the present value column = $ 615,367.55

Point b-2

YES, the decision has changed and US Gold Mine should be selected as it has a higher NPV