ENSC 201: Nineteenth Century English Literature

Lecture 4: Jane Austen

`Sense and Sensibility’

By Jane Austen

Mrs. Dashwood — the second wife of Henry Dashwood, who is left in difficult financial straits by the death of her husband. She is 40 years old at the beginning of the book.

Henry Dashwood — a wealthy gentleman who dies at the beginning of the story. The terms of his estate prevent him from leaving anything to his second wife and their children. He asks John, his son by his first wife, to look after (meaning ensure the financial security of) his second wife and their three daughters.

John Dashwood – the son of Henry Dashwood by his first wife. He intends to do well by his half-sisters, but has a keen sense of avarice and is easily swayed by his

wife, Fanny Dashwood.

Henry Dashwood

Fanny Dashwood

Mrs Dashwood IMrs Dashwood II

John Dashwood

Elinor, Mariane and Margaret Dashwood

£

John Dashwood’s problem is to calculate the present worth of an annuity of £100 settled on his widowed step-mother.

Is it better to give her £1 500 right now, or promise her £100 a year and take the risk that she’ll live an excessively long life?

£100

£1,500

1,500 > 100(P/A,i,N)

N?

For what value of N (the additional years we expect Mrs Dashwood to live) is it the case that

Suppose Mr Dashwood can invest his money at 5% interest…

The critical question is, for what value of N is

1 500 > 100(P/A, 5%, N)?

N 15 20 25 26 27 28 29

100(P/A,5%,N)

1038

1246

1409

1437 1464 1489 1514

Suppose on the other hand Mr Dashwood can invest his money at 10% interest…

The critical question is now, for what value of N is

1 500 > 100(P/A, 10%, N)?

N 15 20 25 30 40 50 100

100(P/A,10%,N)

761 851 908 942 978 991 999

This is a place where we could use the formula for capitalised cost:

PV = A/i

So in this case, PV = 100/0.1 = 1,000 pounds.

By putting £1,000 in the bank now, John Dashwood can ensurehis step-mother gets her £100 annuity forever.

Other Common Forms of Annuity

4. You get a regular salary and a 10% raise every year(or a 10% cut every year)

Too hard for Appendix B

Define a growth-adjusted interest rate io: io = (1+i)/(1+g) - 1

Then (P/A, g, i, N) = (P/A, io, N)/(1+g)

And if i = g, P =NA/(1+g)

Sample problem: I get to choose between a job in industry with a starting salary of $50,000 and 5% raises every year

Or a job in academia where I get $70,000 right away, but never get a raise.

If I can invest all my income at 10% interest, how long will it be before the present value of the industrial job exceeds the present value ofthe academic job?

5. A generous but eccentric uncle gives you $1 000 every leap year

Several alternatives to find present worth:

a)Use (P/F, i, N) on each payment (tedious if there are a lot)

b)Use j = (1+ i)4 – 1 to get a quadrennial interest rate, then use (P/A, j, N/4)

c)Use (A/F, i, 4) to turn the first payment to an annuity, then use (P/A,i,N)

Comparing projects based on Annual Worth

If most of our cash flows are annual, it’s easier to convert one-timeexpenses to their annual equivalent.

Also, you may want to know ``How much will I have to spend aweek?’’ rather than ``What is the present worth of my annual salary?’’

Comparing projects on this basis will always give the same result ascomparison based on present worth or future worth.

ExampleA company wants to expand its capacity. It is considering two alternatives:

1.Construct a new building, at a cost of $2 000 000. Annual maintenance costs will be $10 000. The building will need to be painted every 15 years at a cost of $15 000.

2. Construct a smaller new building now, and another, smaller one in 10 years. The first building costs $1 250 000 to build and $5 000 a year to maintain. The addition will cost $1 000 000 to build, and once it’s built, the two buildings together will cost $11 000 to maintain. Fifteen years after the addition, and every fifteen years after that, the new buildings will be painted at a cost of $15 000.

Assume an interest rate of 15%. Compare the annual cost of the two alternatives.