Solution

Question 1

Floyd's best option is the one that maximizes the present value of his net income after adjusting for the cost of the training program and the raise it would produce.  The table below summarizes the calculations:

Since Program A has the highest present value of the three options, it's Floyd's best choice.  Even though Program B produces a higher income in period 1, its high cost in period 0 keeps its present value below that of Program A.

The problem can also be set up in net terms by comparing both options to Floyd's default, or "business as usual," situation.  In that case, the table would look like this:

Since Program A produces the largest net gain relative to Floyd's default, as before it's the best choice. The two approaches are equivalent: they will always give identical answers about which policy is best.

Question 2

Floyd's optimal consumption bundle given that he enrolls in Program A can be found as follows.  His intertemporal budget constraint has the usual form:

I0 + I1/(1+r) = C0 + C1/(1+r)

The left-hand side is the present value of his net income stream and has already been calculated above: it's $61.4k.  Using that information and inserting the interest rate allows the budget constraint to be written as shown:

$61.4k = C0 + C1/1.1

Since Floyd wants twice as much consumption in period 0 as in period 1, he will choose:

C0 = 2*C1 or C1 = 0.5*C0

Using this to eliminate C1 from Floyd's budget constraint gives the value of C0:

$61.4k = C0 + (0.5*C0)/1.1

$61.4k = C0*(1 + 0.5/1.1)

$61.4k = C0*1.45

C0 = $61.4k/1.45 = 42.2k

Floyd's consumption in period 1 will be:

C1 = 0.5*C0 = 21.1k

Question 3

Since his consumption in period 0 is considerably larger than his net income after paying for the program, he is borrowing.  The amount is $42.2k - ($30k - $5k) = $17.2k.  With interest, in period 1 he'll need to reply $17.2k*1.1 = $18.9k.  After deducting that from his net period 1 income of $40k, he'll $21.1k left over to spend, which is exactly his optimal value of C1.