Learning rate

Captain Kitts has designed a new type of sailing boat, for which the cost of the first boat to be produced has been estimated as follows.
Materials 5,000
Labour (800 hrs ? $5 per hr) 4,000
Overhead (150% of labour cost) 6,000

It is planned to sell all the yachts at full cost plus 20%. An 80% learning curve is expected to apply to the production work. The management accountant has been asked to provide cost information so that decisions can be made on what price to charge.

(a) What is the separate cost of a second yacht?

(b) What would be the cost per unit for a third and a fourth yacht, if they are ordered separately later on?

(c) If they were all ordered now, could Captain Kitts quote a single unit price for four yachts and eight yachts?

Solution
Cumulative units— Cumulative avge time per unit-Cumulative TT Incremental total time
1————————————-800.0 ————————–800.0 – – – –nil
2————————————-640.0 ————————1,280.0———480.0
4————————————–512.0———————— 2,048.0———768.0
8————————————-409.6————————-3,276.8 ——–1,228.8

(a) Separate cost of a second yacht
Materials 5,000
Labour (480 hrs ? $5) 2,400
Overhead (150% of labour cost) 3,600
Total cost 11,000

(b) Cost of the third and fourth yachts-also this looks confusing using two yachts material price and deducting forth yachts’ labor and overhead?
Materials cost for two yachts 10,000
Labour (768 hours ? $5) 3,840
Overhead (150% of labour cost) 5,760 Total cost 19,600

Cost per yacht (?2) 9,800

i used this way to find the cost of 3rd yachts-is this way correct?
Total time for 4—–2048
total time for 1——–800
total time for 3——-1248

so incremental total time(1280-1248)=32

Material-(5000*3)-15000
labor(32*5)—160
overhead(160*150%)-240
total cost-15400