Next: Lecture 3

Assignment for Week 3

Read Chapter 5 of Fraser, Bernhardt, Jewkes and Tajima; do Problems 5.2, 5.4, 5.8, 5.15, 5.21, 5.31. (If you have the first edition of the text, Fraser, Bernhardt and Jewkes, you should do problems 5.2, 5.4, 5.7, 5.11, 5.13, and 5.20)
For this week's assignment, I'd like you to evaluate the numerical values of the (x/y, i, N) factors used in your calculations, though you should defer this evaluation to the last stage.

Model Answers

Problem 5.31

One problem with this question is that the IRR for each model appears to be lower than the MARR, suggesting that you shouldn't buy any of them. However, the question also says that you have to buy one of them. This implies that there's some unspecified benefit to having a heating system that isn't included in the question. Various ways of dealing with this include:

adding a large positive number to each calculation, representing this benefit. (The same positive number each time, of course.)
Using PW instead of IRR (though the question does ask for IRR)
Doing an incremental analysis

Any of these methods will give the same result. Let's try the third: make a table showing the increment from A to B:

Year	Model A	Model B	Increment
0	-500	-3600	-3100
1	-300	500	800
2	-300	500	800
...	...	...	...
9	-300	500	800
10	-300	1500	1800

The IRR of the increment is then calculated as

3100=800(P/A,i,10)+1000(P/F,i,10)

which can be solved to give IRR=23.64%. This is greater than the MARR, so we should upgrade from A to B. We next look at the upgrade from B to C:

Year	Model B	Model C	Increment
0	-3600	-4000	-400
1	500	1000	500
2	500	-3000	-3500
3	500	1000	500
...	...	...	...
9	500	1000	500
10	1500	2000	500

This does not follow the patern of a simple investment, so we use the ERR instead of the IRR:

400(F/P,ERR,10)+3500(F/P,ERR,8)=500(F/P,12%,9)+500(F/A,12%,8)

From which ERR=8.34%. This is less than the MARR, so we don't upgrade to Model C, but buy Model B.

John Jones
Fri, Jan 14, 2000